SOLUTION: Mary needs to go to Jane’s house. Mary drives 4mph going uphill, goes 6mph on flat ground and goes 12mph downhill. It takes her 1 hour to do the trip. How far is Jane’s house?

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Question 163973: Mary needs to go to Jane’s house. Mary drives 4mph going uphill, goes 6mph on flat ground and goes 12mph downhill. It takes her 1 hour to do the trip. How far is Jane’s house?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Mary needs to go to Jane’s house. Mary drives 4 mph going uphill, goes 6 mph
on flat ground and goes 12 mph downhill. It takes her 1 hour to do the trip.
How far is Jane’s house?
:
Let d = distance to house
;
Divide the distance into 4 + 6 + 12 = 22 units
:
The distance at each speed:
4%2F22 = .182d; distance at 4 mph
6%2F22 = .273d; distance at 6 mph
12%2F22 = .545d; distance at 12 mph
:
Write a time equation, Time = dist/speed
%28.182d%29%2F4 + %28.273d%29%2F6 + %28.545d%29%2F12 = 1
Clear the denominator multiply equation 12
3(.182d) + 2(.273d) + .545d = 12
:
.546d + .546d + .545d = 12
;
1.64d = 12
d = 12%2F1.64
d = 7.3 miles
:
Interesting that this is the same distance if you just averaged the 3 speeds
22%2F3 = 7.33 mi; in 1 hr, the distance would 7.33 mi