SOLUTION: Sheri travelled to her cottage and back home again. Her cottage is 90 km from her home. She averaged 20km/h faster on the trip there than the return trip. Determine Sheri’s aver

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Question 1160492: Sheri travelled to her cottage and back home again. Her cottage is 90 km from her home.
She averaged 20km/h faster on the trip there than the return trip. Determine Sheri’s average speed on
the trip to the cottage if the total time there and back was 1.85 hours.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Since the problem asks for her speed going to the cabin, let that be the variable:
x = speed going in km/h

Her speed returning is 20km/h less:
x-20 = speed returning

Write expressions (time = distance divided by speed) for the amounts of time (hours) on the two legs of the trip:
90/x = time going
90/(x-20) = time returning

The total time was 1.85 hours:

90%2Fx%2B90%2F%28x-20%29+=+1.85

Solve using basic algebra... multiply everything by the common denominator, x(x-20):

90%28x-20%29%2B90x+=+1.85%28x%29%28x-20%29

You will get a quadratic equation which, because the numbers are not "nice", will very probably not be able to be solved by factoring. Use the quadratic formula, or a tool like a graphing calculator.