152E- Speed, Time and Distance

152- Speed, Time and Distance

 

Speed, time and distance Based problems are Frequently asked in CAT,CSAT,SSC,Banking and various other competition exams. So it becomes necessary for us to learn this topic. We will move with this topic from the basics.

SPEED:

Speed of a vehicle is defined as the distance covered by that vehicle in total time.

Speed = Distance/time

PROBLEMS BASED ON SPEED, TIME AND DISTANCE:

Generally in exams of SSC, Banking questions on speed, time and distance are very easy as compared to CAT and various other Management Exams ranging from SNAP,NMAT etc.

Questions Asked in SSC Are Having a Statement like

Q. A person moves a distance of 5 km at a speed of 10km/hr by foot and then he hired a cab for a distance of 15km at a speed  of 45 km/hr then he boarded on a train for a distance of 100km at speed of 50km/hr. find the average speed of that person?

A. In order to solve this type of Problem first we should keep this in our mind that average speed = Total Distance travelled/Total time taken to travel that distance.

So, Let us start solving this problem Total Distance Travelled by the person = (5+15+100)km = 120km.

Time Taken by the person to move that distance = for finding the time taken we need to find individual time taken by to person on moving by foot, travelling in cab and finally in train.

For that We will use the formula  time = Distance/Speed.

Time taken by him will be = 5/10 + 15/45 + 100/50 = 17/6hr.

Average Speed = Total Distance/Total Time.

Av. speed= 120×6/17 =   42.35km/hr. is our answer

Train Problems

The basic equation in train problem is the same Speed=Distance/Time

The following things need to be kept in mind while solving the train related problems.

·         When the train is crossing a moving object, the speed has to be taken as the relative speed of the train with respect to the object.

·         The distance to be covered when crossing an object, whenever trains crosses an object will be equal to: Length of the train + Length of the object

Examples on Speed, Time and Distance

1) A train covers a distance in 50 min, if it runs at a speed
of 48kmph on an average. The speed at which the train must run
to reduce the time of journey to 40min will be.

Solution::
Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=40/60hr=2/3hr
New speed = 40* 3/2 kmph= 60kmph

2) Vikas can cover a distance in 1hr 24min, by covering 2/3 of the distance at 4 kmph and the rest at 5kmph, the total distance is?

Solution::
Let total distance be S
total time=1hr24min
A to T :: speed=4kmph
diistance=2/3S
T to S :: speed=5km
distance=1-2/3S=1/3S
21/15 hr=2/3 S/4 + 1/3s /5
84=14/3S*3
S=84*3/14*3
= 6km

Alternate Solution:

Let total distance be x

2/3 distance covered at 4kmph then distance time taken = 2x/3 × ¼ or 2x/12

1/3 distance covered at 5kmph then distance time taken = 1x/3 × 1/5 or 1x/15

Total time taken 1 hr 24 minutes or 7/5 hour

Now 2x/12 + x/15 = 7/5,

LCM 60, 10x+4x or 14x/60 = 7/5,

70x=420 and x = 6 km

3) Walking at ¾ of his usual speed, a man is late by 2 ½ hr. the usual time is.

Solution::
Usual speed = S
Usual time = T
Distance = D
New Speed is ¾ S
New time is  = 4/3 T
4/3 T – T = 5/2
T=15/2 = 7 ½

4) A man covers a distance on scooter, had he moved 3kmph
faster he would have taken 40 min less. If he had moved
2kmph slower he would have taken 40min more. What is the distance?

Solution::
Let distance = x m
Usual rate = y kmph
x/y – x/y+3 = 40/60 hr
2y(y+3) = 9x ————–1
x/y-2 – x/y = 40/60 hr y(y-2) = 3x —————–2

divide 1 & 2 equations
by solving we get x = 40

5) Excluding stoppages, the speed of the bus is 54kmph and
including stoppages, it is 45kmph, for how many min does the bus
stop per hr.

Solution::
Due to stoppages,it covers 9km less.
Time taken to cover 9 km is [9/54 *60] min = 10min

6) Two boys starting from the same place walk at a rate of
5kmph and 5.5kmph respectively. What time will they take to be
8.5km apart, if they walk in the same direction

Solution::
The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs

7) 2 trains starting at the same time from 2 stations 200km
apart and going in opposite direction cross each other at a
distance of 110km from one of the stations. What is the ratio of
their speeds.

Solution::
In same time ,they cover 110km & 90 km respectively
so ratio of their speed =110:90 = 11:9

8) Two trains start from A & B and travel towards each other at
speed of 50kmph and 60kmph resp. At the time of the meeting the
second train has travelled 120km more than the first. What was the distance
between them?

Solution::

Let the distance travelled by the first train be x km
then distance covered by the second train is x + 120km
x/50 = x+120 / 60
x= 600
so the distance between A & B is x + x + 120 = 1320 km

9) A thief steals a car at 2.30pm and drives it at 60kmph. the
theft is discovered at 3pm and the owner sets off in another car
at 75kmph when will he overtake the thief

Solution::
Let the thief is overtaken x hrs after 2.30pm
distance covered by the thief in x hrs = distance covered by
the owner in x-½ hr
60x = 75 ( x- ½)
x= 5/2 hr
thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm

10) In covering distance, the speed of A & B is in the ratio
of 3:4.A takes 30min more than B to reach the destination. The time
taken by A to reach the destination is.

Solution::
Ratio of speed = 3:4
Ratio of time = 4:3
let A takes 4x hrs, B takes 3x hrs
then 4x-3x = 30/60 hr
x = ½ hr
Time taken by A to reach the destination is 4x = 4 * ½ = 2 hr

Q1. A train is traveling at the rate of 45 km/hr. How many seconds, it will take to cover a distance of 4/5 Km?

a) 36     b) 64     c) 90     d) 120

Q2. A train 180 m long moving at the speed of 20 m/sec overtakes a man moving at a speed of 10 m/sec in the same direction. The train passes the man in:

a) 6 sec     b) 9 sec     c) 18 sec     d) 27 sec

Q3. The distance between two cities A and B is 330 km. A train starts from A at 8a.m. and travels towards B at 60 km/ hr. Another train starts from B at 9a.m. and travels towards A at 75 km/hr. At what time do they meet?

a) 10am     b) 10.30am     c) 11am     d) 11.30am

Q4. In covering a certain distance, the speeds of A and B are in the ratio of 3: 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is:

a) 1 hour     b) 3/2 hours     c) 2 hours     d) 5/2 hours

Q5. A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in meters) is

a) 600     b) 750     c) 1000     d) 1250

Q6. Two men are standing on opposite ends of a bridge of 1200 meters long. If they walk towards each other at the rate of 5 m/minute and 10 m/minute respectively, in how much time will they meet each other?

a) 60 minutes     b) 80 minutes     c) 85 minutes     d) 90 minutes

Q7. I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?

a) 9.5 minutes     b) 19 minutes     c) 18 minutes     d) 20 minutes

Q8. The length of a train and that of a platform are equal. if with a speed of 90 km/ hr the train crosses the platform in one minute, then the length of the train ( in meters) is:

a) 500     b) 600     c) 750     d) 900

Q9. A train running at 7/11 of its own speed reached a place in 22 hours. How much time could be saved if the train would run at its own speed?

a) 14 hours     b) 7 hours     c) 8 hours     d) 16 hours

Q10. A man can reach a certain place in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. find his speed per hour.

a) 6km/hr     b) 11/2 km/hr     c) 4 km/hr     d) 5 km/hr

Q11. A thief is noticed by a policeman from a distance of 200m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

a) 100 m     b) 190 m     c) 200m     d) 150m

Q12. A and B start at the same time with speeds of 40km/hr and 50 km/hr respectively. If in covering the journey A takes 15 minutes longer than B, the total distance of the journey is:

a) 46 km     b) 48km     c) 50km     d) 52km

Q13. A train running at 7/11 of its own speed reached a place in 22 hours. How much time could be saved if the train would run at its own speed?

a) 14 hours     b) 7 hours     c) 8 hours     d) 16 hours

Q14. A man with 3/5 of his usual speed reaches the destination 5/2 hours late. Find his usual time to reach the destination.

a) 4 hours     b) 3 hours     c) 15/4 hours     d) 9/2 hours

Q15. A man covered a certain distance at some speed. Had he moved 3 km per hour faster, he would have taken 40 minutes less. If he had moved 2 km per hour slower, he would have taken 40 minutes more. The distance (in km) is:

a) 20     b) 35      c) 11/3     d) 40

Q16. A moving train, 66 meters long overtakes another train of 88 meters long, moving in the same direction in 0.168 minutes. If the second train is moving at 30 km per hr, at what speed is the first train moving?

a) 85 km/hr     b) 50 km/hr     c) 55 km/hr     d) 25 km/hr

Q17.  A student rides on bicycle at 8 km/hour and reaches his school 2.5 minutes late. The next day he increases his speed to 10 km/ hour and reaches school 5 minutes early. How far is the school from his house?

a) 5/8 km     b) 8km     c) 5 km     d) 10 km

Q18. A,B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 second, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they next meet at the starting point again?

a) 46 minutes 12 seconds     b) 45 minutes     c) 42 minutes 36 seconds     d) 26 minutes 18 seconds

Q19. A constable is 114 meters behind a thief. The constable runs 21 meters and the thief 15 meters in a minute. In what time will the constable catch the thief?

a) 19 minutes     b) 18 minutes     c) 17 minutes      d) 16 minutes

Q20. Two trains start from stations A and B and travel towards each other at speeds of 50 km/ hour and 60 km/hour respectively. At the time of their meeting, the second train has traveled 120 km more than the first. The distance between A and B is (km):

a) 990 km     b) 1200     c) 1320     d) 1440

Q21. A train takes 18 seconds to pass through a platform 162 m long and 15 seconds to pass through another platform 120 m long. The length of the train (in m) is:

a) 70     b) 80     c) 90     d) 105

Q22. A train moves with a speed of 30 kmph for 12 minutes and for next 8 minutes at a speed of 45 kmph. Find the average speed of the train:

a) 37.5 kmph     b) 36 kmph     c) 48 kmph     d) 30 kmph

Q23. A car completes a journey in 10 hours. If it covers half of the journey at 40 kmph and the remaining half at 60 kmph, the distance covered by car is:

a) 400 km     b) 480 km     c) 380 km     d) 300 km

Q24. A and B run a kilometer and A wins by 25 sec. A and C run a kilometer and A wins by 275 m. When B and C run the same distance, B wins by 30 sec. The time taken by A to run a kilometer is

a) 2 min 25 sec     b) 2 min 50 sec     c) 3 min 20 sec     d) 3 min 30 sec

Q25. Two cars start at the same time from one point and move along two roads at right angles to each other. Their speeds are 36 km/hour and 48 km hour respectively. After 15 seconds the distance between them will be

a) 400 m     b) 150 m     c) 300 m     d) 250 m

Q26. A train passes two persons walking in the same direction at a speed of 3 km/hour and 5 km/ hour respectively in 10 seconds and 11 seconds respectively. The speed of the train is

a) 28 km/hour     b) 27km/hour     c) 25 km /hour     d) 24 km/hour

Q27. In a kilometer race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 meters, the time taken by a to run 1 kilometer is

a) 250 seconds     b) 205 seconds     c) 200 seconds     d) 210 seconds

Q28. Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the second train is 1000 m., its speed is

a) 100 km/hr     b) 120 km /hr     c) 140 km/hr     d) 150 km/hr

Q29. The speeds of A and B are in the ratio 3: 4. A takes 20 minutes more than B to reach a destination. In what time does A reach the destination?

a) 4/3 hours     b) 2 hours     c) 8/3 hours     d) 5/3 hours

Q30. A man covers half of his journey at 6 km/hr and the remaining half at 3 km / hr. His average speed is

a) 9 km/hr     b) 4.5 km/hr     c) 4 km/hr     d) 3 km /hr

Answers 

1 b 2 c 3 c 4 c  5 d 6 b 7b 8 c 9 c 10 d 11. a 12. c 13 c 14 c 15 d 16 a 17 c 18 a 19 a 20 c 21 c 22 b 23 b 24 a 25 d 26 c  27 b 28 b 29 a 30 c