Chapter 11.6, Problem 70PPS

(a)

To determine

To find: total time taken driving to the game and then back home

Answer to Problem 70PPS

The total time taken driving to the game and then back home is $\frac{88x-240}{x^2-3x}$ .

Explanation of Solution

Given:

Distance between home and college football game = 80 miles

Average speed = 68 miles per hour.

Calculation:

Average speed to the game = x miles per hour

Average speed back from the game = (x − 3) miles per hour

Distance between home and college football game = 80 miles

  $Time=\frac{Dis\text{}\tan \text{}ce}{speed}$

Time to the game $=\frac{80}{x}$

Time back from the game $=\frac{80}{x-3}$

Total time is the sum of time to and back from the game.

Total time $=\frac{80}{x}+\frac{80}{x-3}$

Rewriting using LCD: x(x − 3)

  $\frac{80}{x}(\frac{x-3}{x-3})+\frac{80}{x-3}(\frac{x}{x})$

  $\frac{80\left(x-3\right)}{x\left(x-3\right)}+\frac{80x}{x\left(x-3\right)}$

  $\frac{80x-240}{x^2-3x}+\frac{80x}{x^2-3x}$

Adding the numerators

  $\frac{80x-240+8x}{x^2-3x}$

  $\frac{88x-240}{x^2-3x}$

Conclusion:

Therefore, the total time taken driving to the game and then back home is $\frac{88x-240}{x^2-3x}$ .

(b)

To determine

To find: The total time taken driving to the game and then back home.

Answer to Problem 70PPS

Here, the total time taken driving to the game and then back home is $1.3$ hour.

Explanation of Solution

Calculation:

From part (a)

Total time = $\frac{88x-240}{x^2-3x}$

x = 68 miles per hour

  $\frac{88\left(68\right)-240}{{\left(68\right)}^2-3\left(68\right)}=\frac{5984-240}{4624-204}=1.3hour$

Conclusion:

Therefore, the total time taken driving to the game and then back home is

  $1.3$ hour.