Question

Sydney drove at an average speed of 55 mi/h from her home in Philadelphia to visit her sister in Phoenix. She stayed in Phoenix 15 hours, and on the trip back averaged 40 mi/h. she returned home 41 hours after leaving. How many miles is Philadelphia from Phoenix

Answer 1

602.25 miles

Step-by-step explanation:

• Sydney stayed in Phoenix for 15 hours.

• She returned home 41 hours after leaving.

The total time spent travelling = 41 - 15 = 26 hours

• Let the time she used going to Philadelphia = t

,

• Then, the time spent coming back = (26-t) hours

`\text{Distance}=\text{Rate }* Time`

The average speed from her home in Philadelphia to Phoenix = 55 mi/h.

`\text{Distance}=55t`

The average speed from Phoenix back to Philadelphia = 40 mi/h.

`\text{Distance}=40(26-t)`

Since the distance to and fro is the same, we have:

`\begin{gathered} 55t=40(26-t) \\ 55t=1040-40t \\ 55t+40t=1040 \\ 95t=1040 \\ t=(1040)/(95) \\ t\approx10.95\text{ hours} \end{gathered}`

Therefore, the distance of Philadelphia from Phoenix:

`\begin{gathered} D=55t \\ =55*10.95 \\ =602.25\text{ miles} \end{gathered}`