Setting up an equation to find time

Question

You run and bike a total of 23 km in 1.25 hours. You run at 10 km/hr and bike 24 km/hr. Write an equation to find the time you spend running and the time you spend biking.

Answer 1

Let R = time spent running and B = time spent biking. 

 

The problem statement leads to the equation: R + B = 1.25 hrs (total time spent running and biking is 1.25 hrs). 

 

Now, the problem also states that the total distance traveled is 23 km where you biked at a rate of 24 km/hr and you ran at 10 kn/hr. Using the information we can write the following equation to solve for time spent on each activity:

 

10km/hr*(R) + 24km/hr*(B) = 23 km

 

Substituting the first equation into the second allows you to solve for R or B (you now have two equations and two unknowns).