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acoopersmith
07-14-2009, 01:20 PM
Tina hiked up a 15km trail. The return trip took 30 min less due to a rate increase of 1km/hr. How long did the trip take?

I am having trouble setting up the equations. I know rate x time = distance, and the first equation should be :
(r) (15/r) = 15, but then I wind up getting a no answer when I try the 2 nd equation: (r+1)[(15/r+1) - 0.5] = 15. I just think the second one is wrong and I don't know why.

Subhotosh Khan
07-14-2009, 01:27 PM
Tina hiked up a 15km trail. The return trip took 30 min less due to a rate increase of 1km/hr. How long did the trip take?



Start with naming the variables.

Let the length of the trip = d = 15km

uphill speed = r km/hr

downhill speed = r + 1 km/hr

uphill time = 15/r hour

downhill time = 15/(r+1) hr

The return trip took 30 min less

\frac{15}{r-1} \, - \, \frac{15}{r} \, = \, 0.5

Now continue....