Question

Duathlons A duathlon is an event that consists of running and biking. While training for a duathlon, you run and bike a total of 23 kilometers in 1.25 hours. You run at an average speed of 10 kilometers in 1.25 hours. You run at an average speed of 10 kilometers per hour and bike at an average speed of 24 kilometers per hour. Write and solve an equation to find the time you spend running and the time you spend biking.

Short answer

Thetime spent on running0.50 hours.

The time spent on biking 0.75 hours.

Step-by-step solution

Step-1 – Given

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

Step-2 – To determine

We have to find the time spent on running and the time spent on biking.

Step-3 – Calculation

Let us assume that

$t_1$=the time spend on running and$t_2$= the time spend on biking.

The equations for the time spent on running and the time spend on biking using the given information are:

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

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

$\begin{array}{l}{t}_1+t_2=1.25\mathrm{...}\left(1\right)\\ t_1=1.25-t_2\\ \\ d_1+d_2=23\mathrm{...}\left(2\right)\\ s_1{t}_1+s_2{t}_2=23\\ 10t_1+24t_2=23\\ 10\cdot (1.25-t_2)+24t_2=23\left[\text{puttingvalueof}{t}_1\text{from}\mathrm{...}\left(1\right)\right]\\ 12.5-10t_2+24t_2=23\left[\text{distributiveproperty}\right]\\ 12.5+14t_2=23\\ 12.5-12.5+14t_2=23-12.5\left[\text{subtract12.5fromeachside}\right]\\ 14t_2=10.5\\ 14t_2÷14=10.5÷14\left[\text{divideeachsideby14}\right]\\ t_2=0.75\mathrm{...}\left(3\right)\\ \\ \text{from}\mathrm{...}\left(1\right)\text{weget,}\\ t_1=1.25-t_2\\ t_1=1.25-0.75\left[\text{putvalueof}{t}_2\text{from}\mathrm{...}\left(3\right)\right]\\ t_1=0.50\end{array}$

Hence, the time spend on running is 0.50 hours and the time spend on biking is 0.75 hours.