Get comprehensive solutions to your questions with the help of IDNLearn.com's experts. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.
Sagot :
ANSWER
1.2 hours
EXPLANATION
Let x represent the number of hours it takes to complete the paint job.
The fraction of a job done per hour with both of them working is 1/x.
Lyle does 1/3 of the painting in one hour
(For example, if it took 3 hours to paint the room, then in one hour, only 1/3 of the room will be painted. In two hours, 1/3 + 1/3 = 2/3 of the room will be painted. In three hours, 1/3+1/3+1/3=3/3=1 of the room will be painted---completed)
Selena does 1/2 of the painting in one hour.
Therefore, for one hour, the fraction of the Job that Lyle does added with the fraction of the Job that Selena does is equal to 1/x, which is the fraction of the job done with both of them working
1/3 + 1/2 = 1/x
Multiply both sides of the equation by x
x/3 + x/2 = 1
Factor out x from the left side
x(1/3 + 1/2) = 1
Combine fractions. Get a common denominator for 1/3 and 1/2.
LCD of 1/3 and 1/2 is 6. 1/3 is equivalent to 2/6 and 1/2 is equivalent to 3/6.
x(2/6 + 3/6) = 1
x (5/6) = 1
x = 1 * 6/5
x = 6/5
x = 1.2 hours
ALTERNATIVE EXPLANTION:
job = rate · time ⇔ rate = job/time ⇔ time = job/rate
Lyle can do 1 paintjob of the room in 3 hours. Therefore, Lyle's rate is 1/3 paintjob per hour.
Selena can do 1 paintjob of the room in 2 hours. Therefore, Selena's rate is 1/2 paintjob per hour.
Their rate when working together is combined:
rate = 1/3 + 1/2 = 2/6 + 3/6 = 5/6
Since time = job/rate and we are interested in 1 paintjob, then job = 1 and
time = 1 / (5/6) = 6/5 = 1.2 hours
1.2 hours
EXPLANATION
Let x represent the number of hours it takes to complete the paint job.
The fraction of a job done per hour with both of them working is 1/x.
Lyle does 1/3 of the painting in one hour
(For example, if it took 3 hours to paint the room, then in one hour, only 1/3 of the room will be painted. In two hours, 1/3 + 1/3 = 2/3 of the room will be painted. In three hours, 1/3+1/3+1/3=3/3=1 of the room will be painted---completed)
Selena does 1/2 of the painting in one hour.
Therefore, for one hour, the fraction of the Job that Lyle does added with the fraction of the Job that Selena does is equal to 1/x, which is the fraction of the job done with both of them working
1/3 + 1/2 = 1/x
Multiply both sides of the equation by x
x/3 + x/2 = 1
Factor out x from the left side
x(1/3 + 1/2) = 1
Combine fractions. Get a common denominator for 1/3 and 1/2.
LCD of 1/3 and 1/2 is 6. 1/3 is equivalent to 2/6 and 1/2 is equivalent to 3/6.
x(2/6 + 3/6) = 1
x (5/6) = 1
x = 1 * 6/5
x = 6/5
x = 1.2 hours
ALTERNATIVE EXPLANTION:
job = rate · time ⇔ rate = job/time ⇔ time = job/rate
Lyle can do 1 paintjob of the room in 3 hours. Therefore, Lyle's rate is 1/3 paintjob per hour.
Selena can do 1 paintjob of the room in 2 hours. Therefore, Selena's rate is 1/2 paintjob per hour.
Their rate when working together is combined:
rate = 1/3 + 1/2 = 2/6 + 3/6 = 5/6
Since time = job/rate and we are interested in 1 paintjob, then job = 1 and
time = 1 / (5/6) = 6/5 = 1.2 hours
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.
