Chapter 12, Problem 2STP

To determine

To calculate: The person M’s younger brother’s speed.

Answer to Problem 2STP

(H) between $16$ mph and $17$ mph

Explanation of Solution

Given information: The person M’s speed is $21mph$and ride training loop $10$ times, in the same time his brother rides the same distance $8$ times.

Formula used: We know that $s=\frac{d}{t}$ . Where $t$ is the time of travel, $d$ is the distance covered, and $s$ is the speed.

Calculation: Let us assume that, The person M’s younger brother’s speed is $x$

  $mph$ . And the loop’s distance is $y$ miles.

Rewrite the formula for time travel.

  $\begin{array}{l}s=\frac{d}{t}\\ t=\frac{d}{s}\end{array}$

Time taken by The person M and The person M’s younger brother is the same.

  $\frac{10y}{21}=\frac{8y}{x}$

The left side expression is the time taken by The person M and the right-side expression is the time taken by The person M’s younger brother.

Solving for The person M’s younger brother’s speed $x$

  $\begin{array}{l}\frac{10y}{21}=\frac{8y}{x}\\ x=\frac{8y}{10y}\times 21\\ x=16.8\end{array}$

So, The person M’s younger brother’s speed is $16.8$ mph. That lies between $16$ mph and $17$ mph