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Marcus believes he has the makings of a country music star, so he is flying from Baltimore to Nashville, 700 miles away, to try out his luck. The ride there with the wind takes four hours. A few months later almost broke he heads back, on the same plane and the same wind. The flight then, against the wind, takes five hours. What is the speed of the plane and what is the speed of the wind?

Feb 26, 2020

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Let  the normal  rate  of  the  plane  = P

Let the rate of the wind  = W

With the wind, the effective  rate =  (P + W)

Against the wid, the effective rate  is (P  -W)

And  Rate * Time  =  Distance

So

(P + W) * 4   = 700

(P - W)*5  = 700            simplify

4P + 4W  = 700

5P  - 5W   = 700

Multiply  the  first equation   through by  5   and the  second through  by  4

20 P  - 20W  = 3500

20P -   20W =  2800     add these

40P  =  6300     divide  both sides  by  40

P =   157.5  mph

And

4 (157.5) +  4W  =700    divide through by 4

157.5  +  W  = 175   subtract  157.5  from both sides

W =  17.5   Feb 26, 2020