SOLUTION: A Cashier working alone serves 20 clients in 1 hour. A second Cashier serves the same number of clients in 40 minutes. What time will they need serving the 20 clients if they work

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Question 1089802: A Cashier working alone serves 20 clients in 1 hour. A second Cashier serves the same number of clients in 40 minutes. What time will they need serving the 20 clients if they work both?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
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20%2F1%2B20%2F%282%2F3%29

20%2B%283%2F2%29%2A20
20%2B30
50-------------fifty clients in an hour

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x time, if 20 clients
50x=20
x=20%2F50
x=2%2F5

TIME: %282%2F5%29%2A%2812%2F12%29=24%2F60--------twenty-four minutes

Answer by ikleyn(52814) About Me  (Show Source):
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.
A Cashier working alone serves 20 clients in 1 hour. A second Cashier serves the same number of clients in 40 minutes.
What time will they need serving the 20 clients if they work both?
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In this problem, let us call this work, serving 20 clients, as "one job".

Then the first cashier makes 1%2F60 of the job per minute. It is his rate of work.

The second cashier makes 1%2F40 of the job per minute. It is his rate of work.

When they work together, their combined rate of work is the sum of individual rates, i.e. 1%2F60+%2B+1%2F40 = 2%2F120+%2B+3%2F120 = 5%2F120 = 1%2F24.

Thus we get that the two cashiers, working together, make 1%2F24 of the job per minute.

Now it is clear to you that it will take 24 minutes for both to serve 20 clients.


The problem is solved.

It is a typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


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