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.
To solve this problem, we can first find the ratio of their speeds by dividing Adam's time by Grampy Sampy's time:
Adam's speed = 1 lap / 50 seconds = 1/50 lap/second
Grampy Sampy's speed = 1 lap / 90 seconds = 1/90 lap/second
Now, we need to find the time it takes for Adam and Grampy Sampy to meet. Let's call this time "t". During this time, Adam would have moved a distance of (1/50) * t laps, and Grampy Sampy would have moved a distance of (1/90) * t laps.
Since they meet when they are both at the same location on the track, the distances they travel must be equal:
(1/50) * t = (1/90) * t
Now, we can solve for t by cross-multiplying and simplifying:
90 * (1/50) * t = 50 * (1/90) * t
90/50 = 50/90
9/5 = 5/9
So, we see that the equation is true for any value of t. This means that Adam will be next even with Grampy Sampy after any amount of time, including 0 seconds. Therefore, the answer is 0 seconds.