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.
:
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/((s-2))}}} = {{{13/((s+2))}}}
:
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