SOLUTION: please help me solve this questions,, 1) A main natural gas pipeline feeds into three smaller pipelines, each of which is 2.6 km longer than the main pipeline. If the total leng

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Question 506190: please help me solve this questions,,
1) A main natural gas pipeline feeds into three smaller pipelines, each of which is 2.6 km longer than the main pipeline. If the total length of the four pipelines is 35.4 km, what is the length of each section of the line?

2) A ski lift takes a skier up a slope at 50m/min. The skier skis down the slope at 150m/min. If one round trip takes 24 minutes, how long is the slope?
Answer by Sarah900(12) (Show Source):
You can put this solution on YOUR website!
1) We are going to call the unknown length of the pipe x so
Main Pipeline length= x
Length of 1 of the smaller pipelines = x+2.6
Total length= x+3(x+2.6)= 35.4
distribute and solve for x
x+3x+7.8=35.4
4x+7.8=35.4
4x=27.6
x=6.9
The main pipeline's length is 6.9.
The length of the smaller pipes is x+2.6 so
6.9+2.6=9.5

2) distance=speed*time
distance up the slope= speed(up)*time(up)
distance down the slope= speed(down)*time(down)
Because it is the same slope distance(up)=distance(down)
speed(up)*time(up)=speed(down)*time(down)
We are going to call the time it takes to go up the slope x so
Time (up)= x
Time (down)= 24-x
Plug in what we know and you have
50x=150(24-x)
Now distribute and solve
50x=3600-150x
200x=3600
x=18
Plug it into our original d=s*t and you get
d=50*18
d=900