SOLUTION: Please help me set this up in an equations and solve. I am terrible at word problems. Thank you Flying with the wind, a small plane travels 150 miles in 2 hours. Against the

The other tutor's solution is wrong

Two ways to do it:

1.  In your head with no algebra
2.  Using algebra

1. In your head:

It took the plane a total of 5 hours to go 300 miles.  It gained
the same amount of time flying with the wind as it lost flying 
against it, so it is the same as if it went 300 miles with no 
wind, so in still air the plane can fly 300÷5 or 60mph.  Since 
it went 150 miles in 2 hours, that was 75 miles per hour.  So 
the wind increased its speed by 15 mph, so that's the speed of 
the wind.  Answer: 15mph.

2.  Using algebra:

Make this chart

                    Distance      Rate      Time
With the wind         
Against the wind      

We are given the distances and the times, so fill those in


                    Distance      Rate      Time
With the wind          150                    2
Against the wind       150                    3

Let x = the speed of the plane in still air:
Let y = the speed of the wind.

Flying with the wind, the speed is found by adding the wind's
speed to the plane's, or x+y

Flying against the wind, the speed is found by subtracting the
wind's speed from the plane's, or x-y.

Fill those in:


                    Distance      Rate      Time
With the wind          150        x+y         2
Against the wind       150        x-y         3

Now use Distance = (Rate)(Time)

            150 = (x+y)(2)
            150 = (x-y)(3)

            150 = 2(x+y)
            150 = 3(x-y)

            150 = 2x + 2y
            150 = 3x - 3y

Divide the first equation through by 2
Divide the second equation through by 3

             75 = x + y
             50 = x - y

Add the two equations term by terms:

            120 = 2x

Divide by sides by 2

             60 = x

So the plane goes 60mph in still air.

Substitute x=60 in one of the equations, say the
first one:

            75 = x + y
            75 = 60 + y
            15 = y

Edwin