11. Time and Distance, Quantitative Aptitude, Civil Service Examination,RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan) PDF Download

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
 

Answer : Option D

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
 

Answer : Option A

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.
 

Answer : Option D

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
 

Answer : Option D

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
 

 
Answer : Option D

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
 

Answer : Option B

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
 

Answer : Option D

Explanation :

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

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

Answer : Option A

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
 

Answer : Option C

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. 
 

Answer : Option C

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