Problema Solution
Currently you are using two sprinkler systems and you need to analyze these systems. Together, the to two systems water in 1.5 hours. Sprinkler System B by itself takes 4 hours longer than sprinkler system A by itself.
How long does each system take to water the orchard alone?
Now that you have the rates of each individual system, we need o determine the combined rate. the two system together take 1.5 hours to water the orchard, so the rate is:
1/(3/2)=1/(3/2) * (2/3)/(2/3)=2/3 orchards/hour
Answer provided by our tutors
let
a = the hours that the system A need to water the orchard alone
the rate of system A is: 1/a orchards per hour
b = the hours that the system B need to water the orchard alone
the rate of system b is: 1/b orchards per hour
the together rare is: 2/3 orchards/hour
Sprinkler System B by itself takes 4 hours longer than sprinkler system A by itself:
b = a + 4
1/a + 1/b = 2/3
plug b = a + 4 into the last equation:
1/a + 1/(a + 4) = 2/3
by solving we find:
a = 2 hr
click here to see the step by step solution of the equation:
b = 2 + 4
b = 6 hr
system A needs to 2 hours to water the orchard alone.
system B needs to 4 hours to water the orchard alone.