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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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      Log On

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Question 662380: 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 josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the lift in km/hr
+5s+ = speed skiing in km/hr
Let +t+ = time to go up mountain on lift in hrs
+3%2F4+-+t+ = time spent skiing in hrs
---------
Equation for lift:
(1) +7%2F4+=+s%2At+
Equation for skiing:
(2) +7%2F4+=+5s%2A%28+3%2F4+-+t+%29+
------------------------
(1) +t+=+%287%2F4%29%2A%281%2Fs%29+
Substitute this into (2)
(2) +7%2F4+=+5s%2A%28+3%2F4+-+%287%2F4%29%2A%281%2Fs%29+%29+
(2) +7%2F4+=+%281%2F4%29%2A%28+15s+-+7%2Fs%29+
(2) +7+=+15s+-+7%2Fs+
(2) +7s+=+15s%5E2+-+7+
(2) +15s%5E2+-+7s+-+7+=+0+
Use the quadratic equation to solve for s in km/hr
Have to run- good luck