jack starts at...

Question

Jack starts at the peak of Mt.McKinley, which has an elevation of 20,320 feet above sea level . Jack travels down the mountain, decreasing his elevation at a constant rate of 4 feet per second. Jill starts at the bottom of the mountain, which is at an elevation of 10 feet below sea level. She starts  travelling up the mountain at the same time as Jack starts travelling down. Jill increases her elevation at a constant rate of 1 foot per second.

 

At some point, Jack and Jill will end up at the same elevation at the same time. At what elevation will this happen?

Answer 1

This actually is not as difficult as it seems.  Use the equation rate x time = distance.  We are given each of their rates, they travel the same amount of time, and we know the total distance they cover.

 

Jack distance + Jill distance = 20320 - (-10)

4t + 1t = 20330

5t = 20330

t = 4066 seconds

 

Jack distance = 4t = 4(4066) = 16264 feet

 

But Jack started at 20320 feet elevation

 

20320 - 16264 = 4056 feet elevation where they meet