Question

Theo and dan start at the same location and drive in opposite directions, but leave at different times. When they are 325 miles apart, their combined travel time is 14 hours. If theo drives at a rate of 20 miles per hour and dan drives at a rate of 25 miles per hour, how long had each been driving?

Answer 1

Let x be the time Theo had been driving, and y be the time Dan had been driving, then we can set the following system of equations:

`\begin{gathered} x+y=14 \\ x(20)+y(25)=325 \end{gathered}`

Solving the first equation for x we get:

`x=14-y`

Substituting the above equation in the second equation, and solving for y we get:

`\begin{gathered} (14-y)(20)+25y=325 \\ 280-20y+25y=325 \\ 5y=45 \\ y=9 \end{gathered}`

Then, x=14-9=5.

Therefore, Theo had been driving for 5 hours and Dan had been driving for 9 hours.