P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P…
P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?
12
13
14
15
Solution
Walking in opposite directions, their relative speed = $5+3 = 8$ rounds per hour, so they meet 8 times per hour. From 5:00 to 7:00 a.m. (2 hours) they meet $8\times2 = 16$ times. In the first 20 minutes (5:00-5:20) they meet at 7.5-min and 15-min marks - that is 2 meetings. The remaining meetings between 5:20 and 7:00 = $16 - 3 = 13$ (excluding the meetings up to 5:20). Hence 13 times.