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# need help

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An airplane travels 460 miles from San Diego to San Francisco in 2.5 hours, going against the wind. The return trip is with the wind, and takes only 2 hours. Find the rate of the airplane with no wind. Find the rate of the wind.

Jan 14, 2020

#1
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460 miles in 2.5 hours   with a headwind      rate = x - w         w = wind speed    x = speed in still air

460 miles in 2 hours      with a tailwind         rate = x+w

rate * time = distance

DIstance to and from is the same....equal

2.5 (x-w) = 460    expanded   2.5x - 2.5w = 460

2(x+w)    = 460                       2x   + 2w     = 460       two equations two unkonowns    multiply bottom equation by -1.25

-2.5x -2.5w = -575       add top and bottom

- 5 w = -115

w = 23 mph

2.5 (x-w)=460

2.5(x-23) = 460

x = 207 mph

Jan 14, 2020
#2
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Here is another simple way:

460 / 2.5 =184 mph from San Diego to San Francisco.

460 / 2    =230 mph - going back

[184 + 230] / 2 =207 mph - its speed in still air.

[230 - 184 ] / 2 =23 mph - the speed of the wind.

Jan 14, 2020
edited by Guest  Jan 14, 2020