SOLUTION: A roofer requires 15 hours to shingle a roof. And apprentics roofer can do tthe job in 21 hours. How long would it take to shingle the roof if they work together?
Question 619272: A roofer requires 15 hours to shingle a roof. And apprentics roofer can do tthe job in 21 hours. How long would it take to shingle the roof if they work together?
You can put this solution on YOUR website! A roofer requires 15 hours to shingle a roof. And apprentics roofer can do tthe job in 21 hours. How long would it take to shingle the roof if they work together?
------
roofer rate: 1/15 job/hr
apprentice rate: 1/21 job/hr
---
Together rate: 1/x job/hr
------
Equation:
rate + rate = together rate
1/15 + 1/21 = 1/x
----
21x + 15x = 15*21
---
36x = 15*21
x = (5/12)21
x = (5/4)7
x = 35/4 = 8 3/4 hrs (time to do the job together)
=====================
Cheers,
Stan H.
========================
You can put this solution on YOUR website! roofer 1 does the job in 15 hours.
roofer 2 does the job in 21 hours.
the rate that roofer 1 works is equal to 1/15.
the rate that roofer 2 works is equal to 1/21.
when they work together, their rates are additive.
Since Rate * Time = Units, then the equation is:
(1/15 + 1/21) * Time = 1
Time is what you're trying to find.
the number of units produced is equal to 1 (a shingled roof).
first thing you might want to do is to combine those fractions into 1.
if you multiply the first fraction by 7/7 and you multiply the second fraction by 5/5, then the equation will become:
(7/105 + 5/105) * Time = 1
This simplifies to:
(12/105) * Time = 1
multiply both sides of this equation by 105/12 to get:
Time = 105/12
That's your answer which is equivalent to 8.75 hours
i found the common denominator as follows:
1/15 and 1/21 have different denominators that i want to make the same.
15 is equal to 3*5
21 is equal to 3*7
if i multiply 3*5 by 7 and i multiply 3*7 by 5, i will get a common denominator of 3*5*7
that's what i did.
i multiplied 1/15 by 7/7 and i multiplied 1/21 by 5/5
this kept the fractions the same and allowed them to have the same denominator.
(