# CAT Question Bank - Time, Speed & Distance

• @abhisd
Let the total distance b/w home and school be d, and the point they meet (say M) is at a distance x from the school. Let t be the time taken to cover distance d if they travel in car. We will take speed of car as s and walking speed as (s/6).
[H] -----< (d - x) >----< [M] >------< x >----- [S]
we know, d/s = t --- (1)
In the given situation, son walked till M (distance of x) and father drove a distance of (d - x) after they meet. And they reached 30 minutes late by doing so. Remember 10 min was lost in waiting, so 20 mins was lost while travelling.
so, x/(s/6) + (d - x)/s = t + 20
6x/s + d/s - x/6 = t + 20
5x/s + d/s = t + 20 --- (2)
(2) - (1) = 5x/s = 20
x = 4s
So to cover distance x by walking it will take x/(s/6) = 4s/(s/6) = 24 minutes. Car would take 24/6 = 4 minutes to cover this part and hence car has saved 4 + 4 = 8 minutes (onward and return) because of the son walking this part.
Total time lost = Time lost in repair - Time saved by walking
30 minutes = Time lost in repair - 8
Time lost in repair = 38 minutes.

Alternatively, a much faster thought process by Chandra sir (Takshzila)

If son walked for 6t minutes, then the meeting of car and son happens at (10 + 6t) mins past 5:00 am.
In the event of no fault, car would have been at same point, going back, at t mins past 7:00 am.
Thus, (10 + 6t) - t = 30 i.e. t = 4
The bus is 30 mins late after having saved 4 + 4 = 8 mins by not travelling the distance walked by students.
Repair took 38 minutes.

• @rowdy-rathore

9 hours...................................

• @rowdy-rathore

5.....................................................

• @rowdy-rathore

d ..............70

• @rowdy-rathore 20hours is the time.

• @manaswini Rohan's speed is 9 times than sohan.. so when Sohan completes 3 rounds, Rohan completes 3 * 9 = 27 rounds. 27 times ?

• @Rowdy-Rathore 93.75,31.25

106

43

71

142

61

1