Question 266643
OK.  We need to find the lowest number that is divisible by both 40 and 35---in other words, the Least Common Multiple (LCM)
Here's one way to do that(reduce each to prime numbers):
40=2*20=2*5*4=2*5*2*2
35=7*5
Since both contain 5, we need only to use 5 once.
so, we have 7*5*2*2*2=280 sec
In 280 sec, Cory's car completes exactly 8 revolutions
In 280 sec, Melissa's car completes exactly 7 revolutions
Therefore, after 280 sec, they have both returned to the starting point at the same time.

Hope this helps--ptaylor