Find the speed of the plane in still air if velocity of the wind is 55 mph

Question

A plane can fly 620 miles downwind in the same amount of time as it can travel 400 miles upwind.

Answer 1

d = rt    distance = rate*time

 

Downwind:  rate = plane speed plus wind speed = p+55

620 = t(p+55)     {Equation 1}

 

Upwind: rate = plane speed minus wind speed = p-55

400 = t(p-55)      {Equation 2}

 

Clearing the parenthesis on the 2 equations:

pt + 55t = 620

pt - 55t = 400     add equations

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2pt = 1020

pt = 510

 

t = 510/p

 

Substitute back into one of the original equations

 

pt - 55t = 400

p(510/p) - 55(510/p) = 400

510 - 55(510/p) = 400

-55(510/p) = -110

510/p = 2

2p = 510

p = 255 mph