Question

it takes and airplane, flying with the wind, 4 hours to reach boston from denver. when an airplane flew back against the wind it took 5 hours to reach denver from boston.what is the speed of the airplane if the speed of the wind is 50 mph

Answer 1

Answer: 450 mph

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Step-by-step explanation:

a = speed of airplane without any wind

a+50 = speed of the plane with the wind boosting it

distance = rate*time

d = r*t

d = (a+50)*4

This represents the plane traveling 4 hours at the speed of a+50 mph. We don't really care about the distance d.

The other equation to set up is

d = (a-50)*5

which means the plane is going slower at a-50 mph and travels for 5 hours this time.

The system of equations is

`\begin{cases}d = (a+50)*4\\d = (a-50)*5\end{cases}`

Both equations involve the same variables 'a' and d, which allows us to use substitution to solve for 'a' like so

d = (a+50)*4

(a-50)*5 = (a+50)*4

5a-250 = 4a+200

5a-4a = 200+250

a = 450

The speed of the plane, without any wind, is 450 mph