SOLUTION: Jason travels to work on the Northern Freeway. He notices that the difference in time between if he drives 5 mph below the speed limit and if he drives 15 mph below the speed limit

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Question 1102024: Jason travels to work on the Northern Freeway. He notices that the difference in time between if he drives 5 mph below the speed limit and if he drives 15 mph below the speed limit is 2 minutes. Given that the distance for which he uses the freeway is 10 miles, find the speed limit of the freeway.
Found 3 solutions by josgarithmetic, stanbon, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
               SPEED       TIME             DISTANCE
SLOW           r-5         10%2F%28r-5%29           10
SLOWER         r-15        10%2F%28r-15%29           10
DIFFERENCE                 1%2F30

highlight_green%2810%2F%28r-15%29-10%2F%28r-5%29=1%2F30%29
r is the freeway speed limit.

If the algebra steps are done correctly, this should lead to quadratic equation:
r%5E2-20r-2925=0
Factorable, if you don't see that, then using solution to quadratic formula,
discriminant, 400%2B4%2A2925=12100=121%2A100=11%5E2%2A10%5E2;

r=%2820%2B11%2A10%29%2F2
r=%2820%2B110%29%2F2
highlight%28highlight%28r=65%29%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Jason travels to work on the Northern Freeway. He notices that the difference in time between if he drives 5 mph below the speed limit and if he drives 15 mph below the speed limit is 2 minutes. Given that the distance for which he uses the freeway is 10 miles, find the speed limit of the freeway.
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Below speed limit DATA:
dist = 10 miles ; rate = L-5 mph ; time = dist/rate = 10/(L-5) hrs
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Above speed limit DATA:
dist = 10 miles ; rate = L+15 mph ; time = 10/(L+15) hrs
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Equation:
10/(L-5) - 10/(L+15) = 2/60
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5/(L-5) - 5/(L+15) = 1/30
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150(L+15) - 150(L-5) = (L-5)(L+15)
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150*15 + 150*5 = L^2 + 10L - 75
--------
L^2 + 10L - 75 = 20*150
------
L^2 + 10L - 3075 = 0
----
Limit = 55 mph
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Cheers,
Stan H.
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note tutor stanbon uncharacteristically has an error in his work; the answer by the other tutor is the correct one.