Help on an algebra two work problem?

Question

When Jim works alone in the ticket booth, he can collect $50 in 30 minutes. When Jim and Tony work together, they can collect $50 in 10 minutes. How long would it take Tony alone to collect $50?
Please keep in mind that I don't actually just want the answer, I want to understand how to do this type of work problem. Thank you.

Answer 1

OK Ami, what you have to do is break it down to the amount (fraction) of the job that they can do in one unit of time; here minute.

Jim does 1/30 of the job in a minute. Togethet they do 1/10 of the job in a minute.
If Tony takes m minutes alone, he can do 1/m of the job in a minute.

Then just add the amount Jim does to the amount Tony does to get the amount they both do:

1/30 + 1/m = 1/10 and solve for m.

Hope that was the right amount of help you wanted.

Answer 2

$50/30 minutes is the slope of Jim's work.
so y = 5/3x where x is in minutes.

$50/10 minutes is the slope of them working together
so y = 5x where x is in minutes.

To find the slope of Tony substract Jim from both

5-5/3 = 10/3

so Tony's equation is y=10/3x
and if he wanted to college $50 then 50=10/3x
150=10x
and 15=x
it would take him 15 minutes.