Word Problem

Question

At a local fire station they have different lengths of fire hose. the shortest is half the length of the middle sized one, and one fifth of the length of the longest one. If I connect the three different hose lengths together it add up to 120m long. How long is the shortest hose,middle hose and the longest hose.

 

You can only write out the expression cos I can solve it from there.

Answer 1

 

Let:

s = short hose

m = mid-length hose

x = long hose

 

s = m/2 = x/5
Use substitution to solve for each hose length by putting the below equation in terms of one variable.

120 = s + m + x

 

Answer 2

s + m + l = 120

s = 1/2 * m

s = 1/5 * l

 

Isolate the s in equations 2 & 3.

 

m = 2s

l = 5s

 

Plug into eq 1.

 

s + (2s) + (5s) = 120

8s = 120

s = 15

 

m=2(15) = 30

l = 5(15) = 75

 

Check your work.

 

15 + 30 + 75 = 120

120 = 120

 

So the answers are 15,30, and 75.

Answer 3

Define the variables to begin.

 

Let x = the length of the shortest hose.

Therefore, since the middle hose is twice the shortest hose, the middle hose = 2x.

By the same logic, the longest hose is 5x.

 

Do you know how to go from there?