Question 46

A and B walk around a circular track. They start at 8 am from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9:30 am?

Solution

A does 1 round per 30 minutes

B does 1 round per 20 minutes

How many minutes would it take making a round together:

x/30 + x/20 = 1

2x + 3x = 60

5x = 60

x = 12

They meet every 12 minutes.

How many 12 minute periods are there from 8:00 am to 9:30 am

90 minutes, so

90/12

Answer is 7 times they cross each other.

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