Create two equations describing the distance covered in each person and then combine them to form a system of equations.
After 12 seconds.
Practice makes perfect
Both men run with a constant rate. This means we can describe the distance y from the starting line after x seconds with linear functions in slope-intercept form.
y= mx+ b
In this form, m is the slope and b is the y-intercept. In this case, the y-intercept shows the distance from the starting line before they start running. This is b= 2 and b= 5 for Francis and John, respectively.
Francis:& y= mx+ 2
John:& y= mx+ 5
We also have to determine the slope. Francis runs with a constant rate of 1 meter per second which translates to a slope of m= 1. John runs with a constant rate of 0.75 meters per second which translates to a slope of m= 0.75. Now we can complete the equations.
Francis:& y= 1x+ 2
John:& y= 0.75x+ 5
If we combine the equations, we get a system of linear equations. Notice that 1x is the same thing as just x.
y=x+2 y=0.75x+5
By solving this system, we can determine when John catches up with Francis. Since both equations are solved for y, we should use the Substitution Method.
After 12 seconds, Francis will catch up with John.
Extra
Why didnt we calculate y?
Note that we weren't asked how long a distance they have covered when Francis catches up with John meaning we do not have to solve for y in the system.
