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MATH question please help me?
I've never done a kind of problem like this, and I've finished it and want to know if my answer's correct. Can someone tell me the answer to this question please? Thank you so much.
Austin hiked up a mountain trail and camped overnight at the top. The next day he returned down the same trail. His average rate traveling uphill was 1.8 kilometers per hour and his average rate downhill was 2.7 kilometers per hour. If he spent a total of 15 hours hiking, how long was the trail?
Do not do any rounding.
going up and going down is still same distance so he walked two lengths in total.
in general
x=v*t
where x=distance, v=velocity, t=time
so round trip was
x=v1*t1=v2*t2
where
v1=1.8km/h
v2=2.7km/h
we also know total time
t1+t2=15
so we can write t2=15-t1
ans use that in
v1*t1=v2*t2
v1*t1=v2*(15-t1)
v1*t1+v2*t1=v2*15
t1(v1+v2)=v2*15
t1=v2*15/(v1+v2)
t1=15*2.7/(1.8+2.7)
t1=9 hours
t2=15-t1=6 hours
x=v1*t1=1.8*9=16.2 km
or
x=v2*t2=2.7*6=16.2km
The Austin Hiking Group Treks the Llano River.mp4
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