Question

Allen runs at an average rate of 9 mi/hr and walks at a average rate of 3 mi/hr. Write an equation in standard form to relate the times he can spend walking and running if he travels 30 miles. If he walks for 4 hours, for how long will he run?

Answer 1

The equation would be
`30=12+9x`.

Allen will Run for 2 hours.

Explanation:

Given:

Total Distance traveled = 30 miles

Average rate of walking = 3 mi/hr

Average rate of running = 9 mi/hr

Time for walking = 4 hours

W need to find the time for running.

Solution:

Let Number of hrs required for running be 'x'.

Total Distance traveled is equal Distance Traveled in walking plus Distance traveled in Running

But Distance is equal Rate multiplied by Time.

Framing in equation form we get;

Hence Total Distance Traveled = Rate of walking × Hours of walking + Rate of Running × Hours of running.

Substituting the values we get;

`30 = 3*4 +9x\\\\30=12+9x`

Hence The equation would be
`30=12+9x`

Solving above equation we get;

`9x=30-12\\\\9x=18\\\\x=(18)/(9)=2\ hrs`

Hence Allen will Run for 2 hours.