SOLUTION: Hello. My question is about uniform motion. The problem is as follows: Chris and Michelle arrive in North Carolina by plane at 7:00 a.m. After renting their car, they head to

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Question 143737: Hello. My question is about uniform motion. The problem is as follows:
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 bettter 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 isssue, how fast must Chris travel to get to the bottom of the mountain? Does Chris know something that Michelle does not?
My dilemma is: I think the arrival time and slope are irrelevant. I have worked out that Chris knows it's impossible to finish the decent because he has already used his rate of travel on the hills incline. I cannot however figure out how to put my logic into a formula even given that d=rxt. I just don't see it. Please help.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
one way is find out how many minutes is takes to cover 2 mi at 30 mph
:
Time = dist/speed
;
T = 2/30
T = 1/15 hr; 1/15(60) = 4 min, which, as you say, was used up on the 1st mile
:
If you put in a rate equation:
Let x = time required to go down the hill,
:
4 min = 1/15 hr
(x+) = time to cover the two miles
:
Using a rate equation for 30 mph av speed
30 =
30(x+) = 2
30x + 2 = 2
30x = 2 - 2
30x = 0; obviously not a valid solution