Question 619272
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.