Question

At a furniture manufacturer, worker A can assemble a shelving unit in 5 hours. Worker B can assemble the same shelving unit in 3 hours. Which equation can be used to find t, the time it takes for worker A and worker B to assemble a shelving unit together?

Answer 1

Answer:

Worker A and worker B combined will take 1.875 hours to manufacture a furniture.

Explanation:

 Let us find LCM of 3 and 5.

 LCM = 3 x 5 = 15

 So number of furniture manufactured by worker A in 15 hours = 15/5 = 3

Number of furniture manufactured by worker B in 15 hours = 15/3 = 5

Number of furniture manufactured by both workers in 15 hours = 3 + 5 = 8

Time taken to manufacture 1 furniture by both workers, t = 15/8 = 1.875 hours.

 So worker A and worker B combined will take 1.875 hours to manufacture a furniture.

Answer 2

Answer:

We can use $\frac{1}{t} =\frac{1}{5}+ \frac{1}{3}$ equation to solve for t.

Worker A and worker B takes t = 1.875 hours to assemble a shelving unit together.

Step-by-step explanation:

We have to find the equation that can be used to find t, the time it takes for worker A and worker B to assemble a shelving unit together.

So, Worker A and Worker B works at the rate of $\frac{1}{t}$ shelving unit per hour.

Given:  worker A can assemble a shelving unit in 5 hours.  

So, worker A works at a rate of  $\frac{1}{5}$ Hours to assemble a shelving

Also, given: Worker B can assemble the same shelving unit in 3 hours.

So, worker B works at a rate of  $\frac{1}{3}$ Hours to assemble a shelving.

Thus, equation becomes,

$\frac{1}{t} =\frac{1}{5}+ \frac{1}{3}$

Solving we get,

LCM(3,5) = 15

$\frac{1}{t} =\frac{3+5}{15}=\frac{8}{15}$

Solve for t , we get,

$t=\frac{15}{8}=1.875$

Thus, worker A and worker B takes t = 1.875 hours to assemble a shelving unit together.

Thus, We can use $\frac{1}{t} =\frac{1}{5}+ \frac{1}{3}$ equation to solve for t.