Question

Jason can run 4 miles per hour faster than Roger If Jason runs 30 miles in the time it takes Roger to run 18miles how fast is Roger running?

Answer 1

Let's use the variable x to represent Jason's speed and the variable y to represent Roger's speed.

If Jason can run 4 miles per hour faster than Roger, we can write the following equation:

`x=4+y`

For the same time running, Jason runs 30 miles and Roger runs 18 miles, so we have:

`\begin{gathered} \text{distance}=\text{speed}\cdot\text{time} \\ 30=x\cdot t \\ t=(30)/(x) \\ \\ 18=y\cdot t \\ t=(18)/(y) \\ \\ (30)/(x)=(18)/(y) \end{gathered}`

Using the value of x from the first equation, we have:

`\begin{gathered} (30)/(y+4)=(18)/(y) \\ 30\cdot y=18\cdot(y+4) \\ 30y=18y+72 \\ 30y-18y=72 \\ 12y=72 \\ y=(72)/(12) \\ y=6 \end{gathered}`

Therefore Roger's speed is 6 miles per hour.