Question

kathy alone can finish a job in 10 days. Mona can finish the same job in 20 days. if they work together how long will it take to finish the job. How do you solve this?

Answer 1

\[\frac{10\times 20}{10+20}\]is the easy way

Answer 2

1/x + 1/y = 1/t

where:
x = hours one can finish alone
y = hours the other can finish alone
t = hours combined

1/10 + 1/20 = 1/t

t/10 + t/20 = 1
(2t + t)/20 = 1
3t = 20
t = 20/3

Answer 3

no it is not the average of the two numbers,
in this case it is
\[\frac{200}{30}=\frac{20}{3}=6\tfrac{2}{3}\]

Answer 4

@satellite73 how did you come about this method? yes 6 is one of the answer choices but why?

Answer 5

not six, six and two thirds

Answer 6

or if you prefer six hours and 40 minutes

Answer 7

ah. i didn't notice the choice of 20/3. thank you :)

Answer 8

if you do more than one or two of these the method becomes clear and you can to right to the answer.
reasonign as follows:
first person has a rate of
\[\frac{1}{20}\] second has a rate of
\[\frac{1}{10}\] combined rate is
\[\frac{1}{20}+\frac{1}{10}=\frac{10+20}{10\times 20}\] and you want to solve
\[\frac{10+20}{10\times 20}T=1\] solution is
\[T=\frac{10\times 20}{10+20}\]

Answer 9

so if one can do the job in 4 hours and one can do the job is 6 hours together they can do the job in
\[\frac{4\times 6}{4+6}\] hours