# CAT Practice : Speed Time, Races

Pace up and down, count how many times you run into someone else. Fun, isnt it?

## Speed Time - Races

Q.7: A swimming pool is of length 50 m. A and B enter a 300 m race starting simultaneously at one end of the pool at speeds of 3 m/s and 5 m/s. How many times will they meet while travelling in opposite directions before B completes the race?
1. Twice
2. Thrice
3. Once
4. 5 times

Choice B. Thrice

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## Detailed Solution

Let us tabulate this and then see if we can pick a pattern. Let us say the pool starts from P and ends at Q. B being the quicker one will reach Q first. B will reach Q after 10 seconds.

A will take ${50 \over 3}$ = 16.67 seconds to reach Q, so between 10s and 16.67 seconds they meet once.

First, let us have a table where we know times when A, B would be at the end points

A B
Time
(in sec)
Position Time
(in sec)
Position
16.67 Q 10 Q
33.33 P 20 P
50 Q 30 Q
66.67 P 40 P
83.33 Q 50 Q
100 P 60 P

We see that the critical time slots are multiples of 10 seconds and multiples of 16.67 seconds.

So, let us break the time from 0 to 60 seconds into these slots and see in which direction A and B travel.

Time Position A Position B Do they cross?
0 to 10 P to Q P to Q
10 to 16.67 P to Q Q to P Yes
16.67 to 20 Q to P Q to P
20 to 30 Q to P P to Q Yes
30 to 33.33 Q to P Q to P
33.33 to 40 P to Q Q to P Yes
40 to 50 P to Q P to Q
50 to 60 Q to P Q to P

So, they cross each other thrice totally. Between 10 and 16.67 seconds for the first time; between 20 and 30 seconds for the second time; and between 33.33 to 40 seconds for the third time.

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## 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