# Algebra

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During the first part of a trip a canoeist travels 49 miles at a certain speed. The canoeist travels 25 miles on the second part of the trip at a speed of 5mph slower. The total time for the trip is 5hrs. What was the speed on each part of the trip?

• Algebra -

speed on first part --- x mph
time for first part = 49/x hrs

speed of second part = x-5 mph , where x > 5
time for second part = 25/(x-5)

49/x + 25/(x-5) = 5
multiply by x(x-5)
49(x-5) + 25x = 5x(x-5)
49x - 245 + 25x = 5x^2 - 25x
5x^2 - 99x + 245 = 0
x = (99 ± √4901)/10
= 16.9 or 2.9 but x > 5

on the first trip he went at 16.9 mph and on the second part 11.9 mph

WoW! 16.9 mph in a canoe!!
I am a canoist, don't know anybody who can paddle that fast.

• Algebra -

Thank you!

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