Question

A company president flew 720 miles in a corporate jet but returned in a smaller plane that could fly only half as fast. If the total travel time was 6 hours, find the speeds ( in mph) of the planes.corporate jet. mphsmaller plane. mph

Answer 1

From the problem, the distance travelled is 720 miles.

Let 2x be the speed of the corporate jet

and

x be the speed of the smaller plane, since smaller plane can fly half as fast as the corporate jet.

Let y be the travel time of the corporate jet

and 6 - y be the travel time of the smaller plane since the total time is 6 hours

The working equation is :

speed x time = distance

For the corporate plane :

$\begin{gathered} \text{speed}\times\text{time}=\text{distance} \\ 2x\mleft(y\mright)=720 \\ 2xy=720 \\ xy=\frac{720}{2}=360 \end{gathered}$

For the smaller plane :

$\begin{gathered} \text{speed}\times\text{time}=\text{distance} \\ x(6-y)=720 \\ 6x-xy=720 \end{gathered}$

Substitute xy = 360 to the 2nd equation :

$\begin{gathered} 6x-xy=720 \\ 6x-360=720 \\ 6x=720-360 \\ 6x=360 \\ x=\frac{360}{6}=60 \end{gathered}$

x = 60 which is the speed of the smaller plane

The speed of the corporate plane will be :

2x = 2(60) = 120

The answer :

corporate jet = 120 mph

smaller plane = 60 mph