Question

select the correct answer from each drop - down menu. mike drove 40 miles from his home to his office, and he then drove back home using the same route. the average speed on his return trip was 10 miles/hour more than the average speed on his trip to the office. the total time for the trip is represented by this expression, where x is the average speed on the trip from his home to his office. \\(\frac{40}{x}+\frac{40}{x + 10}\\) the average speed on mikes drive home is represented by \\(\boldsymbol{\text{drop - down menu}}\\). when mike drives at an average speed of 55 mile/hour on his way home, it takes him approximately \\(\boldsymbol{\text{drop - down menu}}\\) to drive to work and back.

Explanation:

Step1: Define return speed variable

The problem states \(x\) is the speed to the office, and return speed is 10 mph more. So return speed = \(x + 10\).

Step2: Find speed to office

Given return speed is 55 mph, solve for \(x\):
\(x + 10 = 55\)
\(x = 55 - 10 = 45\)

Step3: Calculate total travel time

Substitute \(x=45\) into the total time formula:
Total time = \(\frac{40}{45} + \frac{40}{55}\)
Simplify each term:
\(\frac{40}{45} = \frac{8}{9} \approx 0.8889\)
\(\frac{40}{55} = \frac{8}{11} \approx 0.7273\)
Sum the values: \(0.8889 + 0.7273 \approx 1.6162\) hours
Convert decimal hours to hours/minutes: \(0.6162 \times 60 \approx 37\) minutes, so total time ≈ 1 hour 37 minutes, or ~1.62 hours.

Answer:

The average speed on Mike's drive home is represented by \(\boldsymbol{x + 10}\)
When Mike drives at an average speed of 55 mile/hour on his way home, it takes him approximately \(\boldsymbol{1.62 \text{ hours (or 1 hour 37 minutes)}}\) to drive to work and back.