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?
Twice
Thrice
Once
5 times
Correct Answer
Choice B. Thrice
Explanatory Answer
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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 = 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.
Answer Choice (B)
Correct Answer: Thrice
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