# CAT Practice : Speed Time, Races

Find the ratio of Tom's and Jerry's speed. Similarly find the ratio of Jerry's and Bill's speed. Given to us is the ratio of Tom's and Bill's speed. Combine all to find the distance!

## Distance between A and B

Q.18: Tom, Jerry and Bill start from point A at the same time in their cars to go to B. Tom reaches point B first and turns back and meets Jerry at a distance of 9 miles from B. When Jerry reaches B, he too turns back and meets Bill at a distance of 7 miles from B. If 3 times the speed with which Tom drives his car is equal to 5 times Bill’s speed, what could be the distance between the points A and B?
1. 40 miles
2. 24 miles
3. 31 miles
4. 63 miles

Choice D. 63 miles

## Detailed Solution

Let the distance between A and B be ‘x’ miles.
Let their speeds be T, J and B in miles/hour

When Tom meets Jerry:
Distance travelled by Tom = x + 9
Distance travelled by Jerry = x – 9
Time taken will be the same => ${{(x + 9) \over T}}$= ${{(x – 9) \over J}}$
Or ${{T \over J}}$ = ${{(x + 9) \over (x - 9)}}$ -- (1)

When Jerry meets Bill:
Distance travelled by Jerry = x + 7
Distance travelled by Bill = x – 7
Time taken will be the same => ${{(x + 7) \over J}}$= ${{(x – 7) \over B}}$
Or ${{J \over B}}$ = ${{(x + 7) \over (x - 7)}}$ -- (2)

Given 3T = 5B
or ${{T \over B}}$ = ${{5 \over 3}}$
From (1) and (2)
${{T \over B}}$ = ${{T \over J}}$ * ${{J \over B}}$
${{5 \over 3}}$ = ${{(x + 9) \over (x - 9)}}$ * ${{(x + 7) \over (x - 7)}}$
5(x - 9)(x - 7) = 3 (x + 9) (x + 7)
5x2 – 80x + 315 = 3x2 + 48x + 189
2x2 – 128x + 126 = 0
x2 – 64x + 63 = 0
x = 63 or x = 1
X has to be 63

Correct Answer: Distance is 63 miles

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

## More questions from Speed Time, Races

"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi