Question

Use variables x and y to set up two equations to solve the given problem

Answer 1

Given:

The first plane is travelling 3.5 times as fast as the second plane.

After travelling in the same direction for 5.5 hours, they are 1265 miles apart.

To find:

The average speed of each plane.

Step-by-step explanation:

Let x be the average speed of the second plane.

So, 3.5x be the average speed of the first plane.

We know that the distance formula is,

`Distance=Speed* Time`

After travelling in the same direction for 5.5 hours,

`\begin{gathered} First\text{ plane's d}istance-Second\text{ planes's distance = 1265} \\ S_1T_1-S_2T_2=1265 \\ 3.5x(5.5)-x(5.5)=1265 \\ 19.25x-5.5x=1265 \\ 13.75x=1265 \\ x=(1265)/(13.75) \\ x=92mph \end{gathered}`

So, the average speed of the second plane is 92mph.

Therefore, the average speed of the first plane will be,

`3.5(92)=322mph`

Final answer:

• The average speed of the first plane is 322mph.

,

• The average speed of the second plane is 92mph.