Chapter 11.4, Problem 43PPE

To determine

The expression that represent the round-trip air time.

Answer to Problem 43PPE

  $\frac{5000r+250000}{r^2+100r}$

Explanation of Solution

Given information:

The groundspeed for jet traffic from Los Angeles to New York City can be about 100 mi/h faster than the groundspeed from New York City to Los Angeles. Let r is a jet’s groundspeed from New York City to Los Angeles. The distance between two cities is about 2500 miles.

Concept used:

The formula for the distance traveled is $d=rt$

Calculation:

Let r is a jet’s groundspeed from New York City to Los Angeles. So, the speed from Los Angeles to New York City would be $\left(r+100\right)$ as it can be 100 mi/h faster than the groundspeed from New York City to Los Angeles.

Now in order to find the expression that represents the total time, use the time-distance formula with the given values as shown below

  $\begin{array}{c}\text{Total time}=\text{Time to fly NY to LA + Time to fly LA to NY}\\ \text{=}\frac{\text{Distance traveled}}{\text{Speed going out}}+\frac{\text{Distance traveled}}{\text{Speed returning back}}\\ =\frac{2500}{r}+\frac{2500}{r+100}\\ =\frac{2500\left(r+100\right)+2500r}{r\left(r+100\right)}\\ =\frac{2500r+250000+2500r}{r^2+100r}\\ =\frac{5000r+250000}{r^2+100r}\end{array}$

Thus, the expression for total time is $\frac{5000r+250000}{r^2+100r}$ .