Chapter 4, Problem 16CR

To determine

To find: the distance run by L.

Answer to Problem 16CR

The correct option is b.

Explanation of Solution

Given information:

L goes to lake at a speed of 10 mi/h and back to home at a speed of 8 mi/h.

Total time taken by L is 27 min.

Given options are

1. 0.4 mi
2. 4 mi
3. 4.5 mi
4. 2.4 mi

Calculation:

Consider the distance run by L be $\mathrm{x}$ mi.

Distance from home to lake will be $\frac{\mathrm{x}}{2}$ mi.

The formula for distance speed is $\frac{\text{distance}}{\text{speed}}=\text{time}$ .

The equation will be $\frac{\frac{\mathrm{x}}{2}}{\text{10}}+\frac{\frac{\mathrm{x}}{2}}{\text{8}}=\frac{27}{60}$ .

Solve the above equation as shown:

  $\begin{array}{c}\frac{\frac{\mathrm{x}}{2}}{\text{10}}+\frac{\frac{\mathrm{x}}{2}}{\text{8}}=\frac{27}{60}\\ \frac{4\cdot \frac{\mathrm{x}}{2}+5\cdot \frac{\mathrm{x}}{2}}{\text{40}}=\frac{27}{60}\\ \frac{\frac{9\mathrm{x}}{2}}{\text{40}}=\frac{27}{60}\\ \mathrm{x}=\frac{27}{60}\times \frac{80}{9}\\ =4\end{array}$

Hence, the distance run by her will be 4 mi.

The correct option is b.