SOLUTION: A cyclist travels 60 km. If he reduces his speed by 2 km/h, he will take one hour longer to complete the trip. What was the original speed of the cyclist?

Question 167528: A cyclist travels 60 km. If he reduces his speed by 2 km/h, he will take one hour longer to complete the trip. What was the original speed of the cyclist?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A cyclist travels 60 km. If he reduces his speed by 2 km/h, he will take one hour longer to complete the trip. What was the original speed of the cyclist?
.
Apply the "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
In our case, we will shift the formula thus:
t = d/r
.
Let x = original speed of cyclist
.
60/(x-2) = 60/x + 1
Multiplying both sides by a common denominator x(x-2)
60x = 60(x-2) + (x-2)x
60x = 60x - 120 + x^2 - 2x
0 = -120 + x^2 - 2x
0 = x^2 - 2x - 120
0 = (x-12)(x+10)
x= {12, -10}
.
We can toss out the negative solution, leaving us with:
x = 12 mph

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