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# 11. Time and Distance, Quantitative Aptitude, Civil Service Examination,RPSC Notes | Study RAS RPSC Prelims Preparation - Notes, Study Material & Tests - UPSC

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In this module we will deal with basic concepts of time and distance, speed, average speed, conversion from km/h to m/s and vice versa. This chapter will form the basis of further concept of relative speed which is used in train and boat problems.

Important Formulas

1. Speed=Distance/Time
2. Distance=Speed × Time
3. Time=Distance/Speed
4. To convert Kilometers per Hour(km/hr) to Meters per Second(m/s) x km/hr=(x×5)/18m/s
5. To convert Meters per Second(m/s) to Kilometers per Hour(km/hr) x m/s=(x×18)/5 km/hr
6. If a car covers a certain distance at x kmph and an equal distance at y kmph, the average speed of the whole journey = 2xy/(x+y) kmph
7. Speed and time are inversely proportional (when distance is constant) ⇒Speed ∝ 1/Time (when distance is constant)
8. If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by them to cover the same distance is 1/a:1/b or b : a

Solved Examples

 1. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? A. 8.2 B. 4.2 C. 6.1 D. 7.2

Explanation :

Distance = 600 meter

time = 5 minutes = 5 x 60 seconds = 300 seconds

Speed = distance/time=600/300=2m/s=(2×18)/5 km/hr=36/5 km/hr=7.2 km/hr

 2. Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart? A. 17 hr B. 14 hr C. 12 hr D. 19 hr

Explanation :

Relative speed = 5.5 - 5 = .5 kmph (because they walk in the same direction)

distance = 8.5 km

Time = distance/speed=8.5/.5=17 hr.

 3. Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance? A. 1 hr 42 min B. 1 hr C. 2 hr D. 1 hr 12 min

Explanation :

New speed = 6/7 of usual speed
Speed and time are inversely proportional.
Hence new time = 7/6 of usual time
Hence, 7/6 of usual time - usual time = 12 minutes
=> 1/6 of usual time = 12 minutes => usual time = 12 x 6 = 72 minutes = 1 hour 12 minutes

 4. A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office? A. 3 km B. 4 km C. 5 km D. 6 km

Explanation :

If a car covers a certain distance at x kmph and an equal distance at y kmph,the average speed of the whole journey = 2xy/(x+y) kmph

Hence, average speed = (2×3×2)/(2+3)=12/5 km/hr .

Total time taken = 5 hours

⇒Distance travelled = (12/5)×5=12 km

⇒Distance between his house and office =12/2=6 km

 5. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him? A. 80 km B. 70 km C. 60 km D. 50 km

Explanation :

Assume that the person would have covered x km if travelled at 10 km/hr

⇒Speed = Distance/Time=x/10..... (Equation1)

Give that the person would have covered (x + 20) km if travelled at 14 km/hr

⇒Speed = Distance/Time=(x+20)/14..... (Equation2)

From Equations 1 and 2,

X/10=(x+20)/14 ⇒14x=10x+200 ⇒4x=200 ⇒x=200/4=50

 6. A car travels at an average of 50 miles per hour for 212 hours and then travels at a speed of 70 miles per hour for 112 hours. How far did the car travel in the entire 4 hours? A. 210 miles B. 230 miles C. 250 miles D. 260 miles

Explanation :

Speed1 = 50 miles/hour

Time1 = 2*(1/2) hour=5/2 hour

⇒ Distance1 = Speed1 × Time1 = (50×5)/2=25×5=125 miles

⇒Speed2 = 70 miles/hour

Time2 = 1*1/2 hour=3/2 hour

Distance2 = Speed2 × Time2 = 70×3/2=35×3=105 miles

Total Distance = Distance1 + Distance2 =125+105=230 miles

 7. Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper? A. 1800 ft B. 2810 ft C. 3020 ft D. 2420 ft

Explanation :

Speed of the sound = 1100 ft/s ⇒Time = 11/5 second

Distance = Speed × Time = 1100 ×11/5=220×11=2420 ft

 8. A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in meters)? A. 1250 B. 1280 C. 1320 D. 1340

Explanation :

Speed = 5 km/hr

Time = 15 minutes = 1/4 hour

Length of the bridge = Distance Travelled by the man

= Speed × Time = 5×1/4 km

=5×1/4×1000 metre=1250 metre

 9. A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is A. 11 hrs B. 8 hrs 45 min C. 7 hrs 45 min D. 9 hts 20 min

Explanation :

Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back
From this, we can understand that time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
In fact, you can do all these calculations mentally and save a lot of time which will be a real benefit for you.

 10.  A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. A. 121 km B. 242 km C. 224 km D. 112 km

Explanation :

distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 - x) hr
Distance covered in  the first half = 21x
Distance covered in  the second half = 24(10 - x)
But distance covered in  the first half = Distance covered in the second half
=> 21x = 24(10 - x) => 21x = 240 - 24x => 45x = 240 => 9x = 48 => 3x = 16 ⇒x=16/3

Hence Distance covered in the first half = 21x=21×16/3=7×16=112 km. Total distance = 2×112=224 km

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