SOLUTION: During the COVID 19 Pandemic, Jose and Clara volunteered to help in the repacking of goods and rice to be given to the their community. Working together, they can finish repacking

Question 1171260: During the COVID 19 Pandemic, Jose and Clara volunteered to help in the repacking of goods and rice to be given to the their community. Working together, they can finish repacking in 5 hours. If Clara works alone on the repacking of goods and rice, it takes her 3 times as long as Jose to complete the repacking. Find the number of hours for Clara alone to finish the repacking. What is also the time for Jose to complete repacking alone?
Found 3 solutions by math_tutor2020, greenestamps, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

x = time it takes Jose to do the job by himself
y = time it takes Clara to do the job by herself
y = 3x since it takes Clara 3 times as long as Jose to do the job alone.

If Jose takes x hours to do the job, then his rate is 1/x of a job per hour.
If Clara takes y hours to do the job, then her rate is 1/y of a job per hour. This is the same as 1/(3x) since y = 3x.

Their combined rate is
1/x + 1/(3x)
3/(3x) + 1/(3x)
(3+1)/(3x)
4/(3x)

Let r be the combined rate. Multiplying this r value by the number of hours it takes for them to work together (5 hours) gets us 1 full job complete.
(combined rate)*(number of hours) = 1 full job
r*5 = 1
5r = 1

Plug in r = 4/(3x) and solve for x
5r = 1
5(4/(3x)) = 1
20/(3x) = 1
20 = 1*3x
3x = 20
x = 20/3
It takes 20/3 hours for Jose to do the job by himself.
Let's multiply by 60 to convert to minutes
20/3 hours = (20/3 hrs)*(60 min/1 hr)
20/3 hours = (20/3*60) min
20/3 hours = (1200/3) min
20/3 hours = 400 min
If you want this in hours,minutes format, then...
400 min = 360 min + 40 min
400 min = (360/60 hr) + 40 min
400 min = 6 hr + 40 min
400 min = 6 hr, 40 min

Let's use this x value to find y
y = 3x
y = 3*(20/3)
y = 60/3
y = 20
It takes Clara 20 hours to do the job by herself.

If you want this in minutes only, then
20 hours = (20 hrs)*(60 min/1 hr)
20 hours = (20*60) min
20 hours = 1200 min
Or you could do
y = 3x
y = 3*(400 min)
y = 1200 min
Either way, Clara takes 1200 minutes if she works alone.

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Answers:
Jose's time if he works alone = 400 minutes = 6 hr, 40 min
Clara's time if she works alone = 1200 minutes = 20 hours

Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!

Clara takes 3 times as long as Jose to do the job.

That means when working together Jose does 3 times as much work as Clara.

So finishing the job together in 5 hours means Jose does 3/4 of the work and Clara does 1/4 of the work.

Since Clara does 1/4 of the job in 5 hours, the amount of time it takes her to do the whole job alone is 5*4 = 20 hours.
Since Jose does 3/4 of the job in 5 hours, the amount of time it takes hims to do the whole job alone is 5*(4/3) = 20/3 hours, or 6 2/3 hours.

Answer by ikleyn(52750)   (Show Source): You can put this solution on YOUR website!
.

            It is good, if you can solve such problems formally, as other tutor showed you.

            Not only it is good, but even it is NECESSARY.

            But such knowledge costs not much, if you can not solve such simple problem mentally in seconds.

As the condition states, Jose works 3 times as productive as Clara. It is the same as to say that Jose itself works as 3 instances of Clara. Or, re-phrasing, 4 (four) instances of Clara complete the job in 5 hours. Hence, Clara, working alone, completes the job in 4*5 = 20 hours. Regarding Jose, he needs only 1/3 of this time, according to the condition, i.e. hours = 6 hours = 6 hours and 40 minutes.

Solved.

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Now you know practically all possible approaches to the problem.

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