SOLUTION: WHILE ROAD TESTING A NEW MAKE OF CAR, THE EDITOR OF A CONSUMER MAGAZINE FINDS THAT HE CAN GO 12 MILES INTO A 2-MILE-PER-HOUR WIND IN THE SAME AMOUNT OF TIME HE CAN GO 13 MILES WITH

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Question 103338: WHILE ROAD TESTING A NEW MAKE OF CAR, THE EDITOR OF A CONSUMER MAGAZINE FINDS THAT HE CAN GO 12 MILES INTO A 2-MILE-PER-HOUR WIND IN THE SAME AMOUNT OF TIME HE CAN GO 13 MILES WITH A 2-MILE-PER-HOUR WIND BEHIND HIM. FIND THE SPEED OF THE CAR IN STILL AIR.
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WHILE ROAD TESTING A NEW MAKE OF CAR, THE EDITOR OF A CONSUMER MAGAZINE FINDS THAT HE CAN GO 12 MILES INTO A 2-MILE-PER-HOUR WIND IN THE SAME AMOUNT OF TIME HE CAN GO 13 MILES WITH A 2-MILE-PER-HOUR WIND BEHIND HIM. FIND THE SPEED OF THE CAR IN STILL AIR.
:
Let s = speed of the car in still air
Then
(s+2) = speed with the wind
and
(s-2) = speed against the wind
:
Write a time equation: Time = Dist/speed
12%2F%28%28s-2%29%29 = 13%2F%28%28s%2B2%29%29
:
Cross multiply:
13(s-2) = 12(s+2)
:
13s - 26 = 12s + 24
:
13s - 12s = 24 + 26
:
s = 50 mph
:
Check solution by finding if, indeed, the times are equal
12/48 = .25 hr
13/52 = .25 hr