SOLUTION: Jessie and Harper left their school at the same time and began travelling down the same road in the same direction. Jessie was travelling at a speed of 65mph while Harper drove at

Question 568435: Jessie and Harper left their school at the same time and began travelling down the same road in the same direction. Jessie was travelling at a speed of 65mph while Harper drove at 70 mph. How many hours was it before Harper was 5 miles ahead of Jessie?
This is what I tried (I have no clue how to even start):
65x = 70(x+5/70)
65x = 70 (x + 1/14)
65x = 70x + 5
-70x -70x
-5x = 5
/-5 /-5
x = -1 hours
I do have access to the answer booklet but it says that the answer is 1, not -1, but it doesn't show how to do it and our teacher expects us to show our work.
Thank you so so much!
Brianna, age 14
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You can use intuition and think that if Jessie is traveling 65 mph, then in one hour, s/he will have gone 65 miles. In that same time, Harper drove at 70 mph, which means that s/he will have gone 70 miles. The difference of these distances is 70 - 65 = 5 miles.

Or you can set up the equation . To get this equation, we basically use the idea that

(Harpers Distance) - (Jessies Distance) = 5 miles

and that

Distance = (Rate) * (Time)

Now solve for x to get

and get the same answer.
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