During the first part of a canoe trip Tim covered 60 km at a

During the first part of a canoe trip, Tim covered 60 km at a certain speed. He then traveled 24 km at a speed that was 4 km/h slower. If the total time for the trip was 8 hr, what was the speed on each part of the trip?

Solution

1st part DATA:
distance = 60 km ; rate = x km/h ; time = d/r = 60/x hrs
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2nd part DATA:
distance = 24 km ; rate = x-4 km/h ; time = d/r = 24/(x-4) hrs
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Equation
time + time = 8 hrs
60/x + 24(x-4) = 8
Multiply thru by x(x-4) to get:
60(x-4) + 24x = 8x(x-4)
15(x-4) + 6x = 2x(x-4)
15x-60 + 6x = 2x^2-8x
2x^2 - 29x + 60 = 0
x = [29 +- sqrt(29^2 - 4*2*60)]/4
x = [29 +- sqrt(361)]/4
x = [29 +- 19]/4
x = 12 or x = 5/2
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solution that gives positive results:
x = 12 km/h (speed on the 1st part)
x -4 = 8 km/h (speed on the 2nd part)