SOLUTION: The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car traveling 20 mph can stop in 20 ft, how many feet will it take

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Question 929035: The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car traveling 20 mph can stop in 20 ft, how many feet will it take the same car to sop when it is traveling 100 mph?
Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113) (Show Source):
You can put this solution on YOUR website!
d:r^2 ---> 20:(20^2) = 100:(x)

20/400 = 100/x
1/20 = 100/x

stopping distance = x = 2000 ft

Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

for tutor @CubeyThePenguin....

(1) Your cryptic calculations with no explanation are of no use to the student who is trying to learn how to solve the problem.

(2) I can't tell what the calculations you show are supposed to be doing to solve the problem. Remember, your purpose as a tutor here is not to show that you know how to solve a problem; your purpose is to help the student learn how to solve the problem.

(3) And in this case, whatever your calculations were supposed to be doing, they gave the wrong answer....

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Informally, the solution is simple. Since the stopping distance varies directly as the square of the speed, a speed 5 times as great means a stopping distance 5^2=25 times as great. ANSWER: 25(20 feet) = 500 feet.

More formally....

Find the constant of proportionality knowing that the stopping distance is 20 feet at 20mph.

Use that constant to find the sopping distance if the speed is 100mph.

ANSWER: 500 feet