Question

Shawna can paint a fence in 3 hours. Kevin can paint the same fence in 4 hours. How long will it take them working together? Which of the following equations could be used to solve this problem?

1/3+1/4=t
(1/3)t+(1/4)t=1
(1/t)3+(1/t)4=1
3t+4t=1

Answer 1

Explanation:

Shawna can do the whole work in 3 hours.

so, in 1 hour she can do 1/3 of the work.

Kevin can do the whole work in 4 hours.

so, in 1 hour he can do 1/4 of the work.

when they are working together, they will spend the same amount of hours to finish the work with their own rate of progress.

so,

(1/3)t + (1/4)t = 1

as when dealing with fractions of the work, the whole work is then represented by "1".

so, the second answer is correct.

and now to solve it :

t/3 + t/4 = 1

t + 3t/4 = 3

4t + 3t = 12

7t = 12

t = 12/7 = 1.714285714... hours

it will take them about 1.7 hours to complete the work together.

Answer 2

Answer:
`1/3+1/4=t`

when they are working together, they will spend the same amount of hours finishing the work at their rate of progress. so,
`(1/3)t + (1/4)t = 1`when dealing with fractions of the work, the whole work is then represented by "
`1`".