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
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(39630) (Show Source): You can put this solution on YOUR website!
SPEED TIME DISTANCE
SLOW r-5 10
SLOWER r-15 10
DIFFERENCE
r is the freeway speed limit.
If the algebra steps are done correctly, this should lead to quadratic equation:
Factorable, if you don't see that, then using solution to quadratic formula,
discriminant, ;
Answer by stanbon(75887) (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
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L^2 + 10L - 75 = 20*150
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L^2 + 10L - 3075 = 0
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Limit = 55 mph
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Cheers,
Stan H.
----------- Answer by greenestamps(13214) (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.