Question 143301: Chris and Michelle arrive in North Carolina by plane at 7:00 a.m. After renting their car, they head towards their hotel. On the way they must pass over an extremely sloped 2 mile hill.
Chris tells Michelle that he is going to average 30 mph for the 2 miles (to the top and back down). Michelle says, “Okay, go for it.”
Chris begins by driving slowly up the hill and reaches the top (1 mile mark) when Michelle tells him, “Chris, you better pick up the pace, it has taken 4 minutes to get to the top and we still have 1 mile to go (down).” Upset Chris says, “Forget it Michelle, I can’t do this.” Michelle says, “Sure you can.” Chris says, “No I can’t.”
If speed and safety were not an issue, how fast must Chris travel to get to the bottom of the mountain? Does Chris know something that Michelle does not?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let's deal in minutes on this problem:
30 mph=(30*1/60 )mi/min=(1/2 )mi/min
Distance(d) equals Rate(r) times Time(t)or d=rt; r=d/t and t=d/r
Also:
Average Rate=(Total Distance)/(Total Time)
Let t=time required to travel downhill
Total time, then, would be (4+t)
So, our equation to solve is:
1/2=2/(4+t) multiply each side by 2(4+t)
(4+t)=4 subtract 4 from each side
t=0 THIS TELLS US THAT HE MUST TRAVEL THE SECOND MILE IN 0 TIME IN ORDER TO HAVE AN OVERALL AVERAGE OF 30 MPH
IF HE WANTS TO AVERAGE 30 MPH OR (1/2)MI/MIN OVER THE TWO MILES, THEN HIS TOTAL TIME HAS TO BE 4 MIN (2/(1/2)) BUT HE ALREADY USED UP HIS 4 MIN IN THE FIRST MILE!!!!!
HOPE THIS HELPS---PTAYLOR
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