I need help with a word problem.

[wieb83]

So I have been working on this problem for a while and I just can't figure out how to get it started. I have tried many different ways to set it up and I have still not figured it out. Please Help!

Problem:

The hiking club set out at 12 noon. The members hiked along a level road at a steady rate of 4 MPH; up a mountain trail at 3 MPH; immediately back down the mountain trail at 6 MPH, and back home along the level road, again at 4 MPH. They got back at 6 PM. How far did the club hike?

Thanks for you help
Amber

 

[skeeter]

let \(\displaystyle d_1\) = one way distance along the level road
\(\displaystyle d_2\) = one way mountain distance

distance/rate = time

\(\displaystyle \frac{d_1}{4} + \frac{d_2}{3} + \frac{d_2}{6} + \frac{d_1}{4} = 6\)

solve for \(\displaystyle d_1 + d_2\) ... total distance traveled will be twice that value.

 

[wieb83]

So I am confused though, if I am setting the problem equal to 6 hours and then we solve for D1 + D2 and that ends up equal to 12 how can that be a distace because that would be 12 hours and that is not a distance??

 

[skeeter]

you have not kept track of your units.

it's not 12 hrs, \(\displaystyle d_1 + d_2 = 12\) miles