Question

Contestants in the Run-and-Bike-a-thon run for a specified length of time, then bikefor a specified length of time. Jason ran at an average speed of 5.4 mi/h and biked atan average speed of 20.6 mi/h, going a total of 14.6 miles. Seth ran at an averagespeed of 10.8 mi/h and biked at an average speed of 18.8 mi/h, going a total of 18miles. For how long do contestants run and for how long do they bike? Round to thenearest hundredth if necessary.Contestants runhour and bikehour.

Answer 1

The contestants ran for an approximate 0.80 hours and biked for 0.5 hours.

Step-by-step explanation:

Distance = Average Speed x Time

• Let the time the contestants spend running = r

,

• Let the time the contestants spend biking = b

Jason

Jason ran at an average speed of 5.4 mi/h and biked at an average speed of 20.6 mi/h, going a total of 14.6 miles.

`5.4r+20.6b=14.6`

Seth

Seth ran at an average speed of 10.8 mi/h and biked at an average speed of 18.8 mi/h, going a total of 18 miles.

`10.8r+18.8b=18`

Next, solve the two equations for r and b.

`\begin{gathered} (5.4r+20.6b=14.6)*2\implies10.8r+41.2b=29.2 \\ 10.8r+41.2b=29.2 \\ 10.8r+18.8b=18 \\ \text{Subtract} \\ 22.4b=11.2 \\ b=(11.2)/(22.4) \\ b=0.5\text{ hr} \end{gathered}`

Next, solve for r.

`\begin{gathered} 10.8r+18.8b=18 \\ 10.8r+18.8(0.5)=18 \\ 10.8r+9.4=18 \\ 10.8r=18-9.4 \\ 10.8r=8.6 \\ r=(8.6)/(10.8) \\ r\approx0.80\text{hrs} \end{gathered}`

The contestants run for an approximate 0.80 hours and biked for 0.5 hours.