One person can do a certain job in ten minutes, and another person can do the same job in fifteen minutes. How many minutes will they take to do the job together?

If x represents how many minutes to do the job together, then how much of the job does the slowest person do?

Question

One person can do a certain job in ten minutes, and another person can do the same job in fifteen minutes. How many minutes will they take to do the job together?

If x represents how many minutes to do the job together, then how much of the job does the slowest person do?

anonymous · Answer

1/10 + 1/15 = 1/y
where y is time to do job together

hero · Answer

That still doesn't answer the question

hero · Answer

She already knows y = 6

anonymous · Answer

I don't get that... sorry!

anonymous · Answer

I still need help.

anonymous · Answer

well - its the way to do first part

anonymous · Answer

y = 6 is the solution of that equation

anonymous · Answer

These are my options:
a) x/15
b) x/10
c) 15/x

hero · Answer

You could also have done it like this: 


$\frac{M \times W}{M + W} = x$
$\frac{10 \times 15}{10 + 15} = x$
$10 \times 15 = 10x + 15x$
$150 = 10x + 15x$
$1 = \frac{10x + 15x}{150}$
$1 = \frac{10x}{150} + \frac{15x}{150}$
$1 = \frac{x}{15} + \frac{x}{10}$

hero · Answer

so if we are going by the first person, which we know did the job in 10 minutes, then they must have only done x/15 of the job

hero · Answer

Remember this is fractions so 

$\frac{x}{15} < \frac{x}{10}$

hero · Answer

So it makes sense

anonymous · Answer

Okay...wow! You're good!

hero · Answer

Also, to check, since we know that x = 6, we can make sure that $\frac{6}{15} + \frac{6}{10} = 1$