Question

Megan and Sam together take 12 minutes to wash a car. Washing the car by herself Megan took 21 minutes. How long would it take Sam to wash the car?

This is how I started:

1/12 = 1/21 + 1/X

1/12 - 1/21 = 1/X

Now what should I do ?? Cross Multiply?

Answer 1

hmm, this is a tricky question, i'm gonna have to think out side the box, give me a moment.

Answer 2

sure take your time :)

Answer 3

wow this actually stumped me, but i would assume that somewhere there is going to be a half in there.

Answer 4

i'd guess it took her 27 minutes, but that is a total wide guess.

Answer 5

@luigi help out budy

Answer 6

@Luigi0210 my bad

Answer 7

Thanks for trying

Answer 8

i would approach from the speed of the persons. Megan x, Sam y.

Answer 9

if they make together speed is x+y. so doing the work 1/(x+y) = 12

Answer 10

make sense?

Answer 11

no

Answer 12

let me sort out...

Answer 13

I got it, do you want to think it over, or just the result?

Answer 14

i want to know how you got the result my test is tomorrow

Answer 15

OK, as I wrote approach it from the speed of the persons. Just this is not KM/hour but 1 carwash / minute. Megan speed is x. And we know that it takes her 21 minutes, this means 1/x = 21.

Answer 16

Sam speed is y and we are looking for 1/y which will give us the time (in minutes) he washed the car.

Answer 17

If we assume that their speed adds together as it is we know when they work together they washed in 12 minutes 1/(x+y) = 12.

Answer 18

Is this logic so far?

Answer 19

yes

Answer 20

OK, now you only have to solve the equations. What is your result?

Answer 21

If
Megan can wash the car in M minutes while working alone
Sam can wash the car in S minutes while working alone

Then
Together, they can wash the car in t minutes while working alone

As represented by the following equation:

\[\frac{MS}{M + S} = t\]

Now in this case

M = x (since it is not given)
S = 21
t = 12 (which means they can do the job together in 12 minutes)

So therefore, plugging the given info in to the equation, we have:

\[\frac{21x}{21 + x} = 12\]

Solve for x

Answer 22

Solving for \(x\) will give how long it takes for Megan to wash the car while working alone.

Answer 23

\(21x = 12(21 + x)\)

\(21x = 252 + 12x\)

\(21x - 12x = 252\)
\((21 - 12)x = 252\)
\((20 + 1 - 10 - 2)x = 252\)
\((20 - 10 + 1 - 2)x = 252\)
\((10 - 1)x = 252\)
\(9x = 252\)
\(x = 252/9\)

Answer 24

Do you have the result? Same as Hero's.

Answer 25

yup thanks guys

Answer 26

the formula for total time is:
T = M * S / (M+S)
12 = 21 * S / (21 + S)
12 * (21 + S) = (21 * S)
252 + 12S = 21S
252 = 9S
S = 252 / 9 minutes
S = 28 minutes

Answer 27

Thanks for all the help !!

Answer 28

good luck on the test

Answer 29

u r welcome

Answer 30

I seem to have mixed up the variables.