Janet, an experienced shipping clerk, can fill a certain order in 3 hours. Tom, a new clerk, needs 4 hours to do the same job. How long does it take them working together?

Question

Janet, an experienced shipping clerk, can fill a certain order in 3 hours. Tom, a new clerk, needs 4 hours to do the same job. How long does it take them working together?

1 Answer

Impact of this question

7615 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-29T20:39:36

$\frac{12}{7} hr$ $12/7 "hr"$

Explanation:

If Janet can do the job in $3$ $3$ hours, then in $1$ $1$ hour she can do $\frac{1}{3}$ $1/3$ of the job. Similarly, if Tom can do the job in $4$ $4$ hours, in $1$ $1$ hour he'll do $\frac{1}{4}$ $1/4$ of the job.

Let's say that the total amount of time they take to do the job working together is $x$ $x$ hours.

We can then write the equation

$\frac{1}{3} x + \frac{1}{4} x = 1$ $1/3x + 1/4x = 1$

because $\frac{1}{3} x$ $1/3x$ is the total time (in hours) that Janet will take, and $\frac{1}{4} x$ $1/4x$ is the total time (in hours) that Tom will take. Since they're working together, we're adding the two times. This is equal to $1$ $1$ because $1$ $1$ represents the whole job.

To solve this equation, rewrite the fractions so they have a common denominator, and find $x$ $x$ .

$\frac{1}{3} x + \frac{1}{4} x = 1$ $1/3x + 1/4x = 1$

$\frac{4}{12} x + \frac{3}{12} x = 1$ $4/12x + 3/12x = 1$

$\frac{7}{12} x = 1$ $7/12x = 1$

$x = \frac{12}{7} hr$ $x=12/7 "hr"$

So, it takes them $\frac{12}{7} hr$ $12/7 "hr"$ or about $1.7 hr$ $"1.7 hr"$ to complete the job working together.

Science

Math

Humanities

... and beyond

Janet, an experienced shipping clerk, can fill a certain order in 3 hours. Tom, a new clerk, needs 4 hours to do the same job. How long does it take them working together?

1 Answer

Explanation:

Related questions

Impact of this question