Question

analiza can paint a room in 3 hours. loeben can do it in 2 hours. walter can do the painting job in 5 hours. if all of them worked together, how long will take them to paint the room? show your solution​

Answer 1

Answer:

This is your answer to the question.

Answer 2

Given:

No. of hours Analiza can paint = 3

No. of hours Loeben can paint = 2

No. of hours Walter can paint = 5

To find:

No. of hours taken if all three worked together.

Solution:

Work done by Analiza in 1 hour = $\frac{1}{3}$

Work done by Loeben in 1 hour = $\frac{1}{2}$

Work done by Walter in 1 hour = $\frac{1}{5}$

Let $x$ be the time taken by all three to complete the painting of room. Amount of work done by all three in 1 hour = Sum of work done individually in 1 hour

$\frac{1}{x}=\frac{1}{3}+\frac{1}{2}+\frac{1}{5}$

The denominators are not same. Hence, we cannot simply add them. So, we take the LCM of 3, 2 and 5.

$LCM(3,2,5)=30$

So, the common denominator is 30. Multiply each denominator with a suitable number in order to result in 30. The numerator is also multiplied with the same number.

$\frac{1}{x}=(\frac{1}{3}*\frac{10}{10})+ (\frac{1}{2}*\frac{15}{15})+(\frac{1}{5}*\frac{6}{6})$

$\frac{1}{x}=\frac{10}{30}+\frac{15}{30}+\frac{6}{30}$

Now, we can add all the fractions together easily because the denomiators are now same.

$\frac{1}{x}=\frac{10+15+6}{30}$

$\frac{1}{x}=\frac{31}{30}$

Taking reciprocal to get the value of $x$

$x=\frac{30}{31}$

$x=0.9$ ≈ $1$ hour

Time taken by all three to complete painting of room is 1 hour.

Time taken by Analiza, Loeben and Walter to complete the painting of room together is 1 hour.