Question

Please help. WILL MEDAL! Mudog can do 8 jobs in 3 days, and Jimmy can do 5 jobs in 2 days. 39 jobs need to be done. Mudog works 3 days and then Jimmy joins in. How many days will both of them have to work together to complete the 39 jobs? @mathmale @sleepyjess @Directrix @mathstudent55 @zepdrix @rebeccaxhawaii

Answer 1

@surjithayer

Answer 2

How many jobs can each person do per day?

Answer 3

\[Rate _{Mudog}=\frac{ 8 jobs }{ 3 days }\]

Answer 4

\[Rate _{Jimmy}=\frac{ 5 }{ 2 }\]

Answer 5

Rateboth=31/6

Answer 6

31/6 ??

Answer 7

\[\frac{ 8 }{ 3 } +\frac{ 5 }{ 2 } = \frac{ 31 }{ 6 }\]

Answer 8

That is both of their rates put together.

Answer 9

Okay, so now you have a rate that you can apply to the amount of jobs that need to be completed.

Answer 10

What do I do next?

Answer 11

Use this formula: \(\text{rate }(r)\times x\text{ days}=\text{jobs completed in } x\text{ days}\)

Answer 12

You already have the rate \(r=\frac{31}{6}\), and the jobs they want completed is \(39\). Now, putting this into the equation, you get\[\frac{31}{6}x=39\]

Answer 13

This doesn't work because "Mudog works 3 days and then Jimmy joins in"

Answer 14

Okay, then calculate how many jobs Mudog completed in 3 days, subtract that number from 39, and calculate again with the new number of jobs instead.

Answer 15

@mathmale What do you think?

Answer 16

Don't forget that Mudog works 3 days BEFORE Jimmy joins in! so take away those jobs from the original total, and then use the _method_ that @kittiwitti1 proposed, you'll just need the new number of jobs remaining.

Answer 17

I've just given kittiwitti1 a medal for 'best explanation," so I'll hold on sharing what I think beyond that.

Answer 18

Thank you @mathmale (:

Answer 19

@okdutchman7 are you confused? I can explain again

Answer 20

I'm a little confused kittiwitt. Can you explain it a different way?

Answer 21

and / or break up the problem into parts.

Answer 22

Sure.
Okay, so Mudog worked 3 days at his rate of 8 jobs in 3 days. Which basically means he finished 8 jobs. Subtract 8 from 39 and you have 31 jobs left to complete.

Now we have to use their daily rate, which is \(R_{Mudog}=\frac{8}{3}\) and \(R_{Jimmy}=\frac{5}{2}\). As you've calculated before, these two rates added together get you a composite rate of \(R_{total}=\frac{31}{6}\).

Answer 23

good so far?

Answer 24

Yes. I understand.

Answer 25

So the answer is 6 days?

Answer 26

Yes, the answer is 6 days ^_^

Answer 27

Thank you!

Answer 28

No problem ^_^
If you need any more help on problems I'll be floating around the Math forums (:\[\text{Happy OpenStudying!}\]