SOLUTION: The rate of a jet is 400 mph in calm air. Traveling with the wind, the jet can fly 2100 miles in the same amount of time as it takes to fly 1900 miles against the wind. Find the ra

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Question 194738: The rate of a jet is 400 mph in calm air. Traveling with the wind, the jet can fly 2100 miles in the same amount of time as it takes to fly 1900 miles against the wind. Find the rate of the wind.
d=rt
calm air = 400 mph
distance with wind = 2100 miles
distance against wind = 1900 miles
2100 = (400+w)*?
1900 = (400-w)*?
I understand that we need to find w(rate of wind), but what's the time? The problem just states that it is the same.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the times are the same, the time is simply "t" for both equations.


So we have the equations

2100=%28400%2Bw%29t

1900=%28400-w%29t



2100=%28400%2Bw%29t Start with the first equation.


2100%2F%28400%2Bw%29=t Divide both sides by 400%2Bw.


t=2100%2F%28400%2Bw%29 Rearrange the equation


------------------------


1900=%28400-w%29t Move onto the second equation


1900=%28400-w%29%282100%2F%28400%2Bw%29%29 Plug in t=2100%2F%28400%2Bw%29


1900%28400%2Bw%29=%28400-w%292100 Multiply both sides by 400%2Bw.


1900%28400%2Bw%29=2100%28400-w%29 Rearrange the terms.


760000%2B1900w=840000-2100w Distribute.


1900w=840000-2100w-760000 Subtract 760000 from both sides.


1900w%2B2100w=840000-760000 Add 2100w to both sides.


4000w=840000-760000 Combine like terms on the left side.


4000w=80000 Combine like terms on the right side.


w=%2880000%29%2F%284000%29 Divide both sides by 4000 to isolate w.


w=20 Reduce.


So the speed of the wind is 20 mph.