Question

If it takes me (Katelin) 15 minutes to do the dishes after dinner, and it takes my sister (Megan) 20 minutes to do the dishes after dinner, how long would it take if we both did it together?
Katelin= 1/15
Megan= 1/20

Answer 1

so far, I have this: Therefore:
1 /15 +1/20 = 1/x

We first find the least common multiple, which is 60:
4/60 + 3/60= 7/60 but i dont think thats right

Answer 2

go right to the answer
\[\frac{20\times 15}{20+15}\]

Answer 3

no it is right, what you have, but you didn't finish it

Answer 4

how?

Answer 5

you found the rate as \(\frac{7}{60}\)
last step is to write
\[\frac{7}{60}t=1\] i.e. rate times time is one job
so
\[t=\frac{60}{7}\]
my method is quicker though, and gives the same answer

Answer 6

i did exactly what you did, but didn't reduce the faction
you added \(\frac{1}{15}+\frac{1}{20}\) first and got \(\frac{7}{60}\)
then take the reciprocal

Answer 7

i wrote
\[\frac{1}{15}+\frac{1}{20}=\frac{20+15}{20\times 15}\] then take the reciprocal and get
\[\frac{20\times 15}{20+15}\]
same answer, just write the answer first and compute second

Answer 8

so would i just say the answer is 7/60 or 20x15/20+15?

Answer 9

if it helps, heres the question:

Write a word problem describing the time it takes to complete this activity individually
and together.

For example, if John takes 2 hours to mow his lawn and it takes his sister, Maria, 4 hours to mow the same lawn, how long would it take John and Maria to mow the lawn together?
Write a rational equation based upon the word problem you created.
Solve the rational equation.

Answer 10

so my equation is 1/15+1/20= 1/x

Answer 11

ok good

Answer 12

when you added you get
\[\frac{7}{60}=\frac{1}{x}\] right?

Answer 13

yeah

Answer 14

ok and your job is to solve for \(x\)

Answer 15

yes

Answer 16

so if
\[\frac{7}{60}=\frac{1}{x}\] then
\[x=\frac{60}{7}\] done!

Answer 17

oh, okay, thanks!!

Answer 18

yw

Answer 19

notice that 60/7 minutes is about 8.6 minutes or 8 minutes 36 seconds

what would be nice is if you can find numbers so the answer is just a simple number like exactly 8 minutes

Answer 20

Thank you!