Question

A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is 4 mph. What is the speed of the flying carpet in still air?

Answer 1

Answer:

$15.2~mph$

Step-by-step explanation:

Let the time flown by the flying carpet be $t$. Then, we have that $(2.4)/t=(1.4)/t+2*4$.

We multiply both sides of the equation by $t$ to get $2.4=1.4+8t$.

We subtract $1.4$ from both sides to get $1=8t$.

We divide both sides of the equation by $t=1/8$.

We know that the speed of the flying carpet in still wind is the average of the rates of the speed of the flying carpet with the wind and against the wind.

The speed with wind is $(2.4)/(1/8)=19.2$mph.

The speed against wind is $(1.4)/(1/8)=11.2$mph.

The speed in still wind is $(19.2+11.2)/2=(30.4)/2=15.2$.

Therefore, the answer is $\boxed{15.2~mph}$ and we're done!