During their training for a cycling competition, Candice and Sabrina rode around a circular track, starting simultaneously from the same point. Candice maintained a quicker speed, finishing each lap in 40 seconds, while Sabrina took 50 seconds for each lap. How many laps had Candice completed by the time they both returned to the starting point together?

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Official Explanation

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To solve this, we first note that Candice completes a lap in 40 seconds. Therefore, she will be back at the starting point after 40 seconds (1 lap), 80 seconds (2 laps), 120 seconds (3 laps), and so on. If we let C represent the number of laps Candice has completed, then her total time can be expressed as 40C seconds. On the other hand, Sabrina takes 50 seconds per lap. Thus, she will return to the starting point after 50 seconds (1 lap), 100 seconds (2 laps), 150 seconds (3 laps),…

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What this question tests

What it tests

Your application of distance = rate × time to trains, boats, and commuters, including relative speed.

Common trap

Mixing units (miles per hour vs. minutes) or averaging speeds — average speed is total distance over total time.