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

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.

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

Thanks

To find out when Adam will be next even with Grampy Sampy, we need to find the time it takes for them to cover a whole number of laps where they meet each other at the same location on the track.

First, let's find the time it takes for Adam to complete one lap and the time it takes for Grampy Sampy to complete one lap. We already know Adam takes 50 seconds, and Grampy Sampy takes 90 seconds.

To find when they will be next even, we need to find the least common multiple (LCM) of their lap times. The LCM is the smallest multiple that both numbers divide evenly into.

To find the LCM of 50 and 90, we can list the multiples:

Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, ...

Multiples of 90: 90, 180, 270, 360, 450, 540, ...

The LCM is the smallest number in both lists that appears. Here, the least common multiple is 450.

So, it will take 450 seconds for Adam to be next even with Grampy Sampy.

Therefore, the answer is a whole number, 450 seconds.