what is jeans and daves equation

Question

jean leaves the trailhead at the dawn to hike 11 miles towards the lake where her friend Dave is camping. at the same time, Dave starts his hike towards the trailhead so that he can meet jean somewhere in the middle. jean is walking uphill, so she averages only 2 miles per hour. Dave is walking downhill, so he averages 3.5miles per hour.

Answer 1

Your question seems ambiguous. If you are asking simply to set up an equation for the situation, it is this:

Since they start at the same time, then when they meet they have walked for the same amount of time. Let the length of the distance that Jean walks be X. Since the distance between them as they start is 11 miles, then the distance that Dave walks is 11 - X.

The time each takes to walk to the meeting place is just the individual distances divided by their respective speeds. I.e. Time = Distance/Speed = Distance/(Distance/Time) = Time.

X miles/2 miles per hour = (11 - X) miles/3.5 miles per hour

Now if you want to solve the thing, you get X=4 miles which is the length that Jean walks. Thus, Dave walks 11 - 4 = 7 miles. Checking the answer, it makes sense. Since Dave walks faster, he must cover a greater distance in the same amount of time that Jean takes. And, not surprisingly, the ratio of their distances is the same as the ration of their speeds.