Question 220651: A bicyclist traveled 280 km at a certain speed. If the speed had been increased by 5 km/h, the trip could have been made in 1 hour less time. Find the actual speed?
I have tried d= r(t) with d=280 and r= x and r=x+5 with time being constant so that 280/x-280/x+5=1. I think I am on the right track , but do not have it quite right. Thanks.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! A bicyclist traveled 280 km at a certain speed. If the speed had been increased by 5 km/h, the trip could have been made in 1 hour less time. Find the actual speed?
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You indeed start with:
d = rt
But, in this case, we are talking about time. Solve the above equation for 't':
t = d/r
.
Let x = actual speed
then
280/x = 280/(x+5) + 1
Multiply both sides by x(x+5)
280(x+5) = 280x + x(x+5)
280x+1400 = 280x + x^2+5x
1400 = x^2+5x
0 = x^2+5x-1400
Factoring:
0 = (x-35)(x+40)
x = {35, -40}
Since the negative solution doesn't make sense, throw it out -- leaving:
x = 35 km per hour
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