SOLUTION: A plane flies 435 miles in the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15 miles per hour, find the speed of the plane in still

Question 994774: A plane flies 435 miles in the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15 miles per hour, find the speed of the plane in still air
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
This is a very common form of uniform travel rates exercise. The solution here will be generalized.

RT=D relates rate (or speed), time, and distance.

VARIABLES

Direction speed time distance WITHWIND r+w t D AGAINSTWIND r-w t d

Find the two expressions, formulas, for t.

Direction speed time distance WITHWIND r+w D/(r+w) D AGAINSTWIND r-w d/(r-w) d

Those two times were given as equal.

The only unknown variable in this equation is r, the rate of the vehicle in still air.

SOLUTION STEPS FOR THE ARITHMETIC

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

A plane flies 435 miles in the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15 miles per hour, find the speed of the plane in still air

Let speed of the plane, in still air be S
Then speed of plane, with a tailwind = S + 15
Speed of plane, with a headwind = S � 15
We then form the following TIME equation:
435(S - 15) = 345(S + 15) ------- Cross-multiplying
435S - 6,525 = 345S + 5,175
435S � 345S = 5,175 + 6,525
90S = 11,700
S, or speed of plane in still air = , or mph
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