   SEARCH HOME Math Central Quandaries & Queries  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.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.