SOLUTION: a hiking club made a trip of 380 km to a base camp in 7h. they traveled 4h on a paved highway and the remainder of the time on a wilderness trail. if the average velocity on the tr

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Question 1201017: a hiking club made a trip of 380 km to a base camp in 7h. they traveled 4h on a paved highway and the remainder of the time on a wilderness trail. if the average velocity on the trail was 25km/h less than that on the highway, find the average velocity and distance traveled on each part of the trip.
Found 3 solutions by greenestamps, ikleyn, josgarithmetic:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Technically, note that you are talking about speeds, not velocities -- unless both the highway and the wilderness trail are straight lines....

Let x be the average speed in mph on the trail; then the speed on the highway was x+25.

4 hours at speed (x+25) plus 3 hours at speed x makes a total distance of 380 km:

4%28x%2B25%29%2B3%28x%29=380
4x%2B100%2B3x=380
7x=280
x=40

ANSWERS:
highway speed: x+25 = 65 mph
hiking speed: x = 40 mph (impossible...!)

Oh, well. It's just a math problem, so the answers don't need to make sense in the real world....

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
a hiking club made a trip of 380 km to a base camp in 7h.
they traveled 4h on a paved highway and the remainder of the time on a wilderness trail.
if the average velocity on the trail was 25km/h less than that on the highway,
find the average velocity and distance traveled on each part of the trip.
~~~~~~~~~~~~~~~~~~ 

r    = the average speed on the trail, in km/h.

r+25 = the average speed on the highway.


Write the total distance equation

    3*r + 4*(r+25) = 380  kilometers.


From the equation, find r

    3r + 4r + 100 = 380

       7r         = 380 - 100 = 280

        r                     = 280/7 = 40.


ANSWER.  40 km/h on the trail;  40+25 = 65 km/h on the highway.

Solved.




Answer by josgarithmetic(39620) About Me  (Show Source):