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| Math Central | Quandaries & Queries |
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Question from Abby, a student: Two bikers race on a circular track. Biker A can circle the track in 8 minutes, and Biker B can circle the track in 6 minutes. From the start of the race, how many minutes will it be before Biker B overtakes Biker A? |
We have two responses for you
Hi Abby,
I can help you get started. You need to look at the rates they travel. Biker A travels at 1/8 of a cycle per minute and biker B travels at 1/6 of a cycle per minute. How much faster is biker B than biker A?
Penny
Abby,
Biker A's speed is 1 lap every 8 minutes, so that is 1/8.
Biker B's speed is 1 lap every 6 minutes, so that is 1/6.
When you multiply speed by time, you get distance. So if we let T = the time in minutes when Biker B passes Biker A, then T x 1/8 is Biker A's distance and T x 1/6 is Biker B's distance.
When Biker B passes Biker A, she has gone lap further than Biker A.
That means Biker A's distance is one less than Biker B's distance.
T(1/8) = T(1/6) - 1
Solve for T.
Cheers,
Stephen La Rocque.
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