Chapter 3.2, Problem 38E

To determine

To calculate : the time spend on running and the time spend on biking.

Answer to Problem 38E

The time spend on running

  $t_1=0.50\text{ hours}$

The time spend on biking

  $t_2=0.75\text{ hours}$

Explanation of Solution

Given information :

Let, $t_1$ be the time spend on running and $t_2$ be the time spend on biking.

Total distance is 23 km and total time is 1.25 hours.

Consider, the equationfor the time spend on running and the time spend on biking.

  $\begin{array}{l}{t}_1+t_2=1.25\mathrm{...}\left(1\right)\\ \\ d_1+d_2=23\mathrm{...}\left(2\right)\end{array}$$$

Calculation :

To find the time spend on running and the time spend on biking,

  $$$\begin{array}{l}{t}_1+t_2=1.25\mathrm{...}\left(1\right)\\ t_1=1.25-t_2\\ \\ d_1+d_2=23\mathrm{...}\left(2\right)\\ s_1{t}_1+s_2{t}_2=23\\ 10t_1+24t_2=23\\ 10\cdot \left(1.25-t_2\right)+24t_2=23\left[\text{putting value of }{t}_1\text{ from }\mathrm{...}\left(1\right)\right]\\ 12.5-10t_2+24t_2=23\left[\text{ distributive property}\right]\\ 12.5+14t_2=23\\ 12.5-12.5+14t_2=23-12.5\left[\text{subtract 12}\text{.5 from each side}\right]\\ 14t_2=10.5\\ 14t_2÷14=10.5÷14\left[\text{divide each side by 14}\right]\\ t_2=0.75\mathrm{...}\left(3\right)\\ \\ \text{from }\mathrm{...}\left(1\right)\text{ we get,}\\ t_1=1.25-t_2\\ t_1=1.25-0.75\left[\text{put value of }{t}_2\text{ from }\mathrm{...}\left(3\right)\right]\\ t_1=0.50\end{array}$

Therefore,

The time spend on running

  $t_1=0.50\text{ hours}$

The time spend on biking

  $t_2=0.75\text{ hours}$