Adam can run a lap on a certain circular track in 50 seconds. Grampy Sampy can run a lap on this

Question

track in 90 seconds. They start at the same location at the same time and move in the same
direction. If they each run at a constant speed, how many seconds will it take before Adam is next
even with Grampy Sampy? If your answer is not a whole number, give it as a decimal.

Answer 1

No. of laps completed by Adam in time t (in seconds) = Na = t/50

No. of laps completed by Grampy in time t = Ng = t/90

Gramps will be "lapped" when one lap behind Adam

Na = Ng + 1

t/50 = t/90 + 1

90t/4500 = 50t/4500 +1
40t/4500 = 1
t = 112.5 seconds
Na = 2.25 laps
Ng = 1.25 laps

Answer 2

Thanks