Problema Solution
A carpenter can build a toolshed three times as
fast as his apprentice. Working together,
they can build the shed in 6 hours. How long wo
uld it take each of them working alone to
build the shed?
Answer provided by our tutors
let
x = the time the carpenter needs to build the shed alone thus the rate of the carpenter is 1/x sheds per hour
3x = the time the apprentice needs to build the shed alone thus the rate of the apprentice is 1/(3x) sheds per hour
together they build the shed in 6 hours thus their rate is 1/6 sheds per hour
1/x + 1/(3x) = 1/6
by solving the equation we find
x = 8 hours
click here to see the step by step solution of the equation
3x = 3*8 = 24 hours
the carpenter needs 8 hours to build the shed alone.
the apprentice needs 24 hours to build the shed alone.