A plane can fly 300 miles downwind in the same amount of time as it can travel 210 miles upwind. Find velocity of wind if plane can fly 225 mph in still air

Question

Solve and verify answer 

Answer 1

distane = rate * time, or time = distance / rate

 

If v is the velocity of the plane, and w the velociyt of the wind, then the total plane velocity downwind is v+w, and the total velocity upwind is v-w

 

The plane flies 300 miles downwind in time t: t=300/(v+w).  In the same amount of time t, it flies 210 miles upwind: t=210/(v-w).

 

Then 300/(v+w) = 210/(v-w).

 

300(v-w) = 210(v+w)

90v = 510w

 

We are given v=225

Then 90*225 = 510w, or w=675/17 mph