SOLUTION: a plane traveled 580 miles to zambaouga and back. the trip there was with the wind. it took 5 hours. the trip back was against the wind. the trip back was 10 hours. find the speed

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Question 1000926: a plane traveled 580 miles to zambaouga and back. the trip there was with the wind. it took 5 hours. the trip back was against the wind. the trip back was 10 hours. find the speed of the plane in still air and the speed of the wind
Found 3 solutions by josgarithmetic, MathTherapy, Alan3354:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!


Assigned Variable Values
system%28t=5%2Cb=10%2Cd=580%29
Think of t as "to, with wind", and b as "back, against wind". 
           rate        time       distance
WITH       r+w          t         d
AGNST      r-w          b         d

Make the system of equations.
system%28%28r%2Bw%29t=d%2C%28r-w%29b=d%29

system%28rt%2Bwt=d%2Crb-wb=d%29

tw=d-tr
w=d%2Ft-tr%2Ft
w=d%2Ft-r
substitute,
rb-%28d%2Ft-r%29b=d
br-db%2Ft%2Bbr=d
2br-db%2Ft=d
2br=d%2Bdb%2Ft
r=%28d%2Bdb%2Ft%29%2F2b
r=%28dt%2Ft%2Bdb%2Ft%29%2F2b
r=%28dt%2Bdb%29%2F%282bt%29----you could use this form;
highlight%28r=d%2F%282b%29%2Bd%2F%282t%29%29----------plane speed absence of any wind, purely in symbols.

Now find wind speed.
w=d%2Ft-r
w=d%2Ft-d%2F%282b%29-d%2F%282t%29, simplest denominator is 2bt;
w=%28d%2Ft%29%282b%2F%282b%29%29-%28d%2F%282b%29%29%28t%2Ft%29-%28d%2F%282t%29%29%28b%2Fb%29
highlight%28w=%282bt-dt-db%29%2F%282bt%29%29---------wind speed in purely symbolic form.

Substitute the given and known values to evaluate r and w.

You also have the answer to many other exercise questions which fit this same travel rates type, because it is solved in symbolic form; just the given values would be different but the same general description is often given.

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

a plane traveled 580 miles to zambaouga and back. the trip there was with the wind. it took 5 hours. the trip back was against the wind. the trip back was 10 hours. find the speed of the plane in still air and the speed of the wind 
Let speed of plane in still air be S, and wind speed, W

With total speed with wind being 116 (580%2F5) mph, we get:

S + W = 116 ------- eq (i)

With total speed against wind being 58 (580%2F10) mph, we get:

S - W = 58 -------- eq (ii)

2S = 174 -------- Adding eqs (i) & (ii)

S, or speed of plane in still air = 174%2F2, or highlight_green%2887%29 mph

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the 2 groundspeeds, upwind and downwind.
The plane's airspeed is the average of the 2.
----
Windspeed = diff between airspeed and groundspeed.