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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.100 (page 709)

Daria can weed the garden in 7 hours, while her mother can do it in 3. How long will it take the two of them to work together?

Short Answer

Expert verified

They take 2.1 hours= 2 hours and 6 minutes to work both together.

Step by step solution

01

Given information

The time taken by the persons to work is given and the time is asked when they both work together.

02

Form the equation and solve

Use the given sentence to form the required equation.

As per the formula, the total time(t) taken by Daria(D) and her mother(M) both together can be determined by $\frac{1}{D} + \frac{1}{M} = \frac{1}{t} . . . . . . . . . . . (1)$ .
Substitute the time taken by Daria and her mother into equation (1) and solve it to find the total time.

$\begin{array}{rcl} \frac{1}{t} & = & \frac{1}{D} + \frac{1}{M} \\ = & \frac{1}{7} + \frac{1}{3} \\ = & \frac{7 + 3}{7 \times 3} \\ = & \frac{10}{21} \\ T & = & \frac{21}{10} \\ = & 2.1 h o u r s \\ = & 2 h o u r s 6 m i n u t e s \end{array}$

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Most popular questions from this chapter

The distance a moving body travels, $d$ , varies directly with the time, $t$ , it moves. The train travels 100 miles in 2 hours.

Write the equation that relates $d a n d t$ .
How many miles would it travel in 5 hours?

Multiply $\frac{72 x - 12 x^{2}}{8 x + 32} . \frac{x^{2} + 10 x + 24}{x^{2} - 36}$

In the following exercise, perform the indicated operation:

$\frac{3}{2 x^{2} + 5 x + 2} - \frac{1}{2 x^{2} + 3 x + 1}$

In the following exercises, divide the rational expressions.

$\frac{\frac{3 b^{2} + 2 b - 8}{12 b + 18}}{\frac{3 b^{2} + 2 b - 8}{2 b^{2} - 7 b - 15}}$

In the following exercise, perform the indicated operation:

$\frac{3 d}{d + 2} + \frac{4}{d} - \frac{d + 8}{d^{2} + 2 d}$

See all solutions

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