SOLUTION: Mark road his new Harley 60 mph for part of the trip and 70 miles per hour for the rest of the trip home from the Shakespeare Festival in Ashland,Oregon. If the entire trip was 25

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Question 1110610: Mark road his new Harley 60 mph for part of the trip and 70 miles per hour for the rest of the trip home from the Shakespeare Festival in Ashland,Oregon. If the entire trip was 250 miles, and he spent twice as much time traveling at the faster speed, how many miles was he able to travel at each rate.
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Mark road his new Harley 60 mph for part of the trip and 70 miles per hour for the rest of the trip home from the Shakespeare Festival in Ashland,Oregon. If the entire trip was 250 miles, and he spent twice as much time traveling at the faster speed, how many miles was he able to travel at each rate.
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slower rate DATA::
rate = 60 mph ; distance = d miles ; time = d/60 hrs
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faster rate DATA:
rate = 70 mph ; distance = 250-d ; time = (250-d)/70 hrs
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Equation::
faster time = 2(slower time)
(250-d)/70 = 2(d/60)
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(250/60d) - (d^2/60) = (140/60)d
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d^2/60 - (110/60)d = 0
d^2 - 110d = 0
d(d-110) = 0
Positive solution::
distance = 110 miles (distance at slower rate)
250-d = 140 miles (distance at faster rate)
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Cheers,
Stan H.
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Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.
x + y = 250                     (1)      (x = the distance traveled at 60 mph)

y%2F70 = 2%2A%28x%2F60%29%29                    (2)      (he spent twice as much time traveling at the faster speed)


x    +   y = 250                (1')
140x - 60y =   0                (2')


Multiply eq(1') by 60 (both sides). You will get


 60x + 60y = 250*60
140x - 60y =      0
-------------------------------Add the equations

200x = 250*60  ====>  2x = 25*6  ====>  x = 25*3 = 75.


Answer.  75 miles at the rate of 60 mph and the rest 250 - 75 = 175 miles at the rate 70 mph.


Check.  75%2F60 = 1.25  hours.   175%2F70 = 2.5 hours = 2 times 1.25 hours.   ! Correct !

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The solution by the other tutor is INCORRECT.