SOLUTION: Bicyclists A and B leave the same point P at the same time at right angles. B travels 7 mph faster than A. After 3 hours they are 39 miles apart. Find the speed of each bicyclist

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Question 118425: Bicyclists A and B leave the same point P at the same time at right angles. B travels 7 mph faster than A. After 3 hours they are 39 miles apart. Find the speed of each bicyclists.
I figured out that the answers are 5 and 12 mph but I can't figure out how to do it algebraically. If you could help that would be great!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Bicyclists A and B leave the same point P at the same time at right angles. B travels 7 mph faster than A. After 3 hours they are 39 miles apart. Find the speed of each bicyclists.
I figured out that the answers are 5 and 12 mph but I can't figure out how to do it algebraically.
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Bike A DATA:
Rate = x mph ; Time = 3 hrs ;distance = rt = 3x miles
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Bike B DATA;
Rate = x+7 mph ; Time = 3 hrs ; distance = rt = 3(x+7) miles
EQUATION:
Use Pythagoras
39^2 = (3x)^2 +(3x+21)^2
39^2 = 9x^2 + 9x^2+126x+21^1
18x^2+126x-1080 = 0
2x^2+14x-120=0
x^2+7x-60=0
x = [-7 +- sqrt(49-4*-60)]/2
x = [-7 + sqrt(289)]/2
Positive answer:
x = [-7 + 17]/2
x = 5
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A's rate = 5 mph
B's rate = 5+7 = 12 mph
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Cheers,
Stan H.