Question

On the way to work Juan carpools with a fellow co-worker then takes the city bus back home in the evening. The average speed of the 20-mile trip is 5 miles per hour faster in the carpool. Write an expression that represents Juan's total travel time.

Answer 1

Answer:

$\frac{40r+100}{r(r+5)}$

Step-by-step explanation:

Let r represent speed in the carpool.

We have been given that on the way to work Juan carpools with a fellow co-worker then takes the city bus back home in the evening. The average speed of the 20-mile trip is 5 miles per hour faster in the carpool.

We know that time is equal to distance over speed.

The total distance is 20 mile. Time taken to travel 20 miles using carpool would be $\frac{20}{r}$

The speed on the bus is 5 miles greater, so it will be $x+5$. Time taken to travel 20 miles using bus would be $\frac{20}{r+5}$

Total time will be equal to sum of both times that is:

$\frac{20}{r+5}+\frac{20}{r}$

Let us simplify our expression.

$\frac{20r}{r(r+5)}+\frac{20(r+5)}{r(r+5)}$

$\frac{20r}{r(r+5)}+\frac{20r+100}{r(r+5)}$

Combine numerator:

$\frac{20r+20r+100}{r(r+5)}$

$\frac{40r+100}{r(r+5)}$

Therefore, our required expression would be $\frac{40r+100}{r(r+5)}$.