Write and solve a rational equation to determine the speed of the wind

Question

A bi-plane can fly 120 mph with no wind. Against the wind the plane travels 84 miles in the same time it takes to fly 108 miles with the wind. Determine the speed of the wind

Answer 1

Hi Taylor,

 

Distance = Rate * Time

 

Time is the same in both of these instances.

 

So Time against the wind = Distance against the wind/rate against the wind

 

And Time with the wind = Distance with the wind/rate with the wind

 

And since both times are the same, we can set these equal:

 

Dist against/rate against = Dist with/rate with

 

Now, let's let W = the speed of the wind.

 

rate against the wind is 120-w

rate with the wind is 120+w

 

This is how you will come up with a rational equation.

 

Dist against/rate against = 84/(120-w)

 

Dist with/rate with =108/(120+w)

 

And these two ratios are equal to each other.  So the rational equation will be

 

  84                 108

--------    = -----------

120-w           120+w

 

 

Now cross-multiply and solve.

 

84(120+w) = 108(120-w)