SOLUTION: Hi. I need help with this word problem. Samantha rides the ski lift to the top of blue mountain, a distance of 1 3/4 kilometers. She then skis directly down the slope. If she skis

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Question 662379: Hi. I need help with this word problem.
Samantha rides the ski lift to the top of blue mountain, a distance of 1 3/4 kilometers. She then skis directly down the slope. If she skis 5 times as fast as the lift travels, and the total trip takes 45 minutes, find the rate at which she skis.
Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Samantha rides the ski lift to the top of blue mountain, a distance of 1 3/4 kilometers. She then skis directly down the slope.
If she skis 5 times as fast as the lift travels, and the total trip takes 45 minutes, find the rate at which she skis.
:
Let s = speed of the lift
then
5s = skiing speed
:
Write a time equation, change 45 min to .75 hrs, speed will be in km/hr
time = dist/speed
1.75%2Fs + 1.75%2F%285s%29 = .75
multiply by 5s to clear the denominators, results:
5(1.75) + 1.75 = 5s(.75)
:
8.75 + 1.75 = 3.75s
:
10.5 = 3.75s
:
s = 10.5/3.75
:
s = 2.8 km/hr is the lift speed
then
5(2.8) = 14 km/h is the skiing speed
:
:
Check this by finding the times up and down
1.75/2.8 = .625 hrs
1.75/14 = .125 hrs
=====================
total time: .75 hrs which is 45min