Question 236571
 During the first part of a trip, a canoeist travels 79 miles at a certain speed. The canoeist travels 2 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip? 
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1st part DATA:
distance = 79 miles ; rate = x mph ; time = d/r = 79/x hrs.
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2nd part DATA:
distance = 2 miles ; rate = x-5 mph ; time = d/r = 2/(x-5) hrs

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Equation:
time + time = 2 hrs
79/x + 2/(x-5) = 2
Multiply thru by x(x-5) to get:
79(x-5) + 2x = 2x(x-5)
79x - 395 + 2x = 2x^2 - 10x
2x^2 -91x + 395 = 0
Use Quadratic Formula to 
get a reasonable value of "x":
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The answers are 4.86 and 40.64
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Neither answer is reasonable for canoeing speed.
It can't be 4.86 because x-5 would be negative.
It can't be 40.64 because canoes don't go that fast.
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Cheers,
stan H.