SOLUTION: A bicycle trip of 120 miles would have taken 3 hours less if the average speed had been increased by 2 miles per hour. Find the average speed of the bicycle.

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Question 164477: A bicycle trip of 120 miles would have taken 3 hours less if the average speed had been increased by 2 miles per hour. Find the average speed of the bicycle.
Found 2 solutions by checkley77, themathprof:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
120/X=[120/(X+2)]+3
X[120/(X+2)+3=120
120X/(X+2)+3X=120
[(120X+3X(X+2)]/(X+2)=120
(120X+3X^2+6X)/(X+2)=120
126X+3X^2=120(X+2)
3X^2+126X=120X+240
3X^2+126X-120X-240=0
3X^2+6X-240=0
3(X^2+2X-80)=0
3(X+10)(X-8)=0
X-8=0
X=8 MPH IS THE SLOWER TRIP.
8+2=10 MPH FOR THE FASTER TRIP.
120/8=15 HOURS.
120/10=12 HOURS.
240/X=27
27X=240
X=240/27
X=8.89 MPH IS THE AVERAGE SPEED.



Answer by themathprof(21) About Me  (Show Source):
You can put this solution on YOUR website!
A bicycle trip of 120 miles would have taken 3 hours less if the average speed had been increased by 2 miles per hour. Find the average speed of the bicycle.
x= avg speed of bicycle
The distance is the same (120) before and after the increase
The Rate changes from x to x+2
Note that in each case the time is Distance/Rate

Rate x Time = Distance
Before increase
x....120/x.....120
After increase
x+2...120/x+2..120

New Time is 3 less
120/(x+2) = 120/x -3
Multiply each term by LCM=x(x+2)
x(x+2)(120)/(x+2) = x(x+2)(120)/x -3(x)(x+2)
Cancel denominators
120x=120(x+2)-3x(x+2)
120x=120x+240-3x^2-6x
0=-3x^2-6x+240
divide by -3
0=x^2+2x-80
Factor right side
0=(x-8)(x+10)
x-8=0 .... x=8 avg speed of bicycle
x+10=0 ... x=-10 (reject, speed can't be negative!)

CHECK
Rate x Time = Distance
Before increase
8....120/8=15.....120
After increase
8+2=10...120/8+2=12..120
Time decreases 3 from 15 to 12
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