The podunk village fire truck has two hoses. the length of hose #1 is 20ft less than 4 times the length of hose #2. the combined length of the two hoses is 380 ft. find the length of the longer hose.

This a system of equations question. What you will do is make an equation comparing the two lengths then make another one as the sum of the lengths.  H1 will stand for hose 1 and H2 will stand for hose 2. 
so our first equation is H1=4*(H2)-20. We know this because H1 is 20 less than 4 times H2. 

Our second equation is H1+H2=380. We know this because the sum of the hoses is 380.

Now we can substitute the H1 in the second equation with 4*(H2)-20. Our new equation then is 4*(H2)-20+H2=380. Solving for H2 we add 20 to both sides of the equation and get 5*(H2)=400. Then we divide both sides by 5 and find that H2=80.

Now we find the length of H1 by plugging in the value H2 into the second equation. We get H1+80=380. subtracting both sides by 80 we find that H1=300. 

If H1=300 and H2=80. The length of the longer hose is 300 feet.