Question

A plane can fly 1020 miles in the same time as it takes a car to go 360 miles. If the car travels 110 mph slower than the plane, find the speed of the plane.

Answer 1

170 mph

Explanation:

Let x mph be the plane's speed.

If the car travels 110 mph slower than the plane, then the car's speed is x - 110 mph.

Plane:

Speed = x mph

Distance = 1,020 miles

Time = t hours

`1,020=x\cdot t\Rightarrow t=(1,020)/(x)`

Car:

Speed = x - 110 mph

Distance = 360 miles

Time = t hours

`360=(x-110)t\Rightarrow t=(360)/(x-110)`

A plane can fly 1020 miles in the same time as it takes a car to go 360 miles, so

`(1,020)/(x)=(360)/(x-110)`

Cross multiply:

`1,020(x-110)=360x\\ \\102(x-110)=36x\\ \\102x-11,220=36x\\ \\102x-36x=11,220\\ \\66x=11,220\\ \\x=170`