A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
Question
A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
Solution
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First, we need to determine the total time that A and B are walking. They start at 8 a.m. and continue until 9:30 a.m., so they are walking for 1.5 hours.
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Next, we need to find out how many rounds they complete in this time. A completes 2 rounds per hour, so in 1.5 hours, A completes 2 * 1.5 = 3 rounds. B completes 3 rounds per hour, so in 1.5 hours, B completes 3 * 1.5 = 4.5 rounds.
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Since A and B are walking in opposite directions, they will cross each other once for each round that they complete. So, we need to add the number of rounds that A and B complete to find out how many times they cross each other.
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Adding these together, A and B cross each other 3 + 4.5 = 7.5 times. However, they can't cross each other half a time, so we round down to the nearest whole number.
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Therefore, A and B cross each other 7 times before 9:30 a.m.
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