# Math Help Online

If you are having any trouble with math at school, you can find online help for math for all grades and college students as well.  Math online help is one of the easiest ways to get the math help you need, every day. There is growing awareness among parents and students on the benefits associated with online live math help. You can learn anytime you want and with great tutors who have worked with hundreds of students like you.

## Free Online Math Help Live

Math online help is as good as or better than face-to-face tutoring. Students interact with their tutors from the comfort of their homes and extensive practice material is available all the time. Homework help is a part of online live math help that all students find especially useful and exam help prepares students for important tests and exams. Using math online help regularly allows the math helper to focus on each student’s strengths and weaknesses and proceed accordingly.

## Solved Examples

Question 1: 8 men and 12 women can finish a piece of work in 10 days while 6 men and 8 women can finish it in 14 days. Find the time taken by the one man alone and that by one women alone to finish the work.
Solution:
Let one man alone can finish the work in x days

and one woman alone can finish the work in y days

Step 1:

One day work of a man = $\frac{1}{x}$

One day work of a woman = $\frac{1}{y}$

Case 1:
8 men and 12 women can finish a piece of work in 10 days

=> $\frac{8}{x} + \frac{12}{y} = \frac{1}{10}$               .......................(1)

Case 2:
6 men and 8 women can finish a piece of work in 14 days

=> $\frac{6}{x} + \frac{8}{y} = \frac{1}{14}$                 .........................(2)

Step 2:
Put $\frac{1}{x}$ = u and $\frac{1}{y}$ = v

(1) => 8u + 12v = $\frac{1}{10}$

=> 10(8u + 12v) = 1

=> 80u + 120v = 1                                    ....................................(3)

and equation (2) implies

6u + 8v = $\frac{1}{14}$

=> 14(6u + 8v) = 1

=> 84u + 112v = 1                                      ...................................(4)

Step 3:
Subtract equation (3) from equation (4)

=> 84u + 112v - (80u + 120v) = 1 - 1

=> 84u + 112v - 80u - 120v = 0

=> 4u - 8v = 0

=> u - 2v = 0

=> u = 2v                                                     ........................................(5)

Step 4:
Put u = 2v in equation (3)

80 * 2v + 120v = 1

=> 160v + 120v = 1

=> 280v = 1

=> v = $\frac{1}{280}$, put in equation (5)

u = 2 * $\frac{1}{280}$

or u = $\frac{1}{140}$

Step 5:
Since, $\frac{1}{x}$ = u and $\frac{1}{y}$ = v

=> $\frac{1}{x}$$\frac{1}{140}$

=> x = 140

and $\frac{1}{y}$ = $\frac{1}{280}$

=> y = 280

Answer: One can  finish a piece of work in 140 days and one woman in 280 days.

Question 2: A closed box has a base twice as long as it is wide. If its volume 124 m cube, find its surface area.

Solution:
Step 1:
Let base (width) of the cube  = x

Then length of the box = 2x

Height of the box = y

[Since the base of the box is a rectangle whose length is twice its width]

Let S be the surface area of the box

=> S = sum of the areas of its six sides    ...................(1)

Step 2:

Area of the top and bottom of the box = 2x2 (each)

Area of the front and back of the box = 2xy (each)

Area of the left and right sides of the box = xy (each)

(1) => S = 2x2 + 2x2 + 2xy + 2xy + xy + xy

=> S = 4x2 + 6xy          .........................(2)

Step 3:

Volume of the box = length * width * height

=> 124 = 2x2 y

=> y = $\frac{124}{2x^2}$ = $\frac{62}{x^2}$

(2) => S = 4x2 + 6xy

=> S = 4x2 + 6x *  $\frac{62}{x^2}$

= 4x2 + 6 *  $\frac{62}{x}$

=> S = $\frac{4x^3 + 372}{x}$ surface area of the box.