You can do it in your head. But your teacher won't accept that. But I'll show you how to do it in your head anyway, then we'll do it by algebra.
In your head:
Their rate of separation is 7-5 or 2 miles an hour. So in 1 hour they would be 2 miles apart. In half an hour they would be 1 mile apart, so in half that time, or 15 minutes, they will be half a mile apart. Answer: 15 minutes.
But, of course, your teacher won't accept that. So,
By algebra:
Let t = the time in hours they both run before Russ is
ahead by mile.
Make this DRT-chart
Distance Rate Time
Russ
Janet
They both ran for t hours. So fill in t for both
their times:
Distance Rate Time
Russ t
Janet t
Now fill in 7 for Russ' rate and 5 for Janet's rate:
Distance Rate Time
Russ 7 t
Janet 5 t
Now use formula DISTANCE = RATE × TIME
t fill in their distances:
Distance Rate Time
Russ 7t 7 t
Janet 5t 5 t
Now the difference between their distances
must equal mile:
Russ' distance MINUS Janet's distance = a mile
So:
7t - 5t =
2t =
Multiply both sides by 2 to clear of fractions:
4t = 1
Divide both sides by 4
t =
That's an hour or 15 minutes.
Edwin