Chapter SH, Problem 1.22EP

a.

To determine

To find: the total distance covered by taxi as per Shannon’ s condition.

Answer to Problem 1.22EP

  $18.85miles$ .

Explanation of Solution

Given:

The maximum amount expends for booking the taxi is under $\$35$ .

Initial fare	$\$2.00$
Mileage charge	$\$1.75$

Calculation:

According to the question, the initial fare for taxi is $\$2.00$ and the mileage charge is $\$1.75$ .

As the maximum amount expends for booking the taxi is under $\$35$ .

Since, the minimum fare for booking taxi is $\$2.00$ , therefore, the rest amount is $\$35-2=\$33$ .

Therefore, the maximum distance covered by taxi is $d_{\max }=\frac{33}{1.75}=18.85\text{miles}$

Therefore, the total distance covered by taxi is $18.85miles$ .

b.

To determine

To check: whether the Samantha has enough money to cover the fare.

Answer to Problem 1.22EP

No.

Explanation of Solution

Given:

The maximum amount expends for booking the taxi by Samantha is $\$21$ .

And the total distance covered is $21miles$ .

Initial fare	$\$2.00$
Mileage charge	$\$1.75$

Calculation:

According to the question, the initial fare for taxi is $\$2.00$ and the mileage charge is $\$1.75$ .

Since, the minimum fare for booking taxi is $\$2.00$ , therefore, the rest amount is $\$21-2=\$19$ .

Therefore, the total fare for covered to $\$21$ by taxi is $21\times 1.75=\$36.75$ .

Therefore, the amount needed to cover the total distance is $\$36.75-\$19=\$17.75$ .

No, the Samantha has not enough money to cover the fare.