Chapter 3.1, Problem 65STP

To determine

Find the time would it take Sancho to ride 30 miles.

Answer to Problem 65STP

Time taken to cover 30 miles is 1 hour 53 minutes. Option A is correct.

Explanation of Solution

Given:

Sancho can ride 8 miles on his bicycle in 30 minutes.

4 Options are:

A: 8 hours; B: 6 hours 32 minutes; C: 2 hours; D: 1 hour 53 minutes.

Concept Used:

Sancho can ride 8 miles on his bicycle in 30 minutes.

We need to find the time needed to ride 30 miles at this rate.

Let the time taken for 30 miles is x minutes.

Set a proportion: $\frac{\text{Distance}\text{in}\text{mile}}{\text{time}\text{in}\text{minutes}}=\frac{8}{30}=\frac{30}{x}$

Calculation:

Let the time taken for 30 miles is x minutes.

Set a proportion: $\frac{\text{Distance}\text{in}\text{mile}}{\text{time}\text{in}\text{minutes}}=\frac{8}{30}=\frac{30}{x}$

  $\begin{array}{l}\frac{8}{30}=\frac{30}{x}[\text{use}\text{cross}\text{multiplication}\text{method}:\frac{a}{b}=\frac{c}{d}\Rightarrow a·d=b·c]\\ 8x=900\\ \frac{8x}{8}=\frac{900}{8}\\ x=112.5\text{minutes}\end{array}$

Time taken to cover 30 miles at the rate 8 miles in 30 minutes is 112.5 minutes.

  $112.5\text{minutes}=\text{1}\text{hour}\text{52}\text{.5}\text{minutes}\approx \text{1}\text{hour}\text{53}\text{minutes}$

Option A is correct.

Thus, time taken to cover 30 miles is 1 hour 53 minutes. Option A is correct.