Working Together - Math Story Problems

Question

Tasha can do a job in 3 hours, and Ben can do the same job in 12 hours. How long will it take the two of them to do the job working together?

Answer 1

Sometimes it is important to have the physical understanding of a problem so that we know where things come from and not just simply blindly apply a formula.

.

Let us call the J the "total job" that needs to be completed. This can be counting beans, for example.

Speed at which Tasha works is J divided by 3 hours or J/3

Speed at which Ben works is J divided by 12 hours or J/12

The combined speed that Tasha and Ben work together is (J/3 +J/12)

But the combined speed of the two together is also equal to J/t, where t is the time that the two take together

Thus:

J/3 + J/12 = J/t

J cancels out and we are left with:

1/3 + 1/12 = 1/t

Therefore, adding the fractions:

5/12 =1/t

or t -12/5

or t= 2 2/5 hours

Once you get the picture of where things come from, then it is appropriate to use shortcuts.

Answer 2

Tasha can do a job in 3 hours, and Ben can do the same job in 12 hours. How long will it take the two of them to do the job working together?

First of all take the time to review the word problem and establish a method of solving the math problem.

Step 1: Word Problem Analysis:

Let T be the time it takes for Tasha to do the job alone.

Let B the time it takes for Ben to do the job alone.

How long take to do the job alone?

We are given that Tasha (T) = 3 hours and Ben (B) = 12 hours

Step 2:

How long will it take the two of them to do the job working together?

We first need to find a common denominator for the fractions.

1/3 + 1/12 the common denominator is 12

1/3 x 12/1 = 12/3 =4 =4/12

1/12 x 12/1=12/12 =1/12

4/12 +1/12 = 5/12

Their combined work rate is 5/12 of the job per hour.

Step 3:

Time is the inverse of the work rate: 1/5/12

Simplify 1/5/12 = 12/5

Convert to mixed number: 12/5 = 2 2/5

Convert the fraction of hour to minutes: 2/5 times 60 = 24 minutes

The time it takes them to complete the job together is 2 hours and 24 minutes.

Mathematical Solution:

It will take Tasha and Ben 2 hours and 24 minutes to complete the job together.

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.

Answer 3

Working together problems can be tricky.

But let x = the number of hours it will take for Tasha and Ben to do the job working together.

Then (1/3) + (1/12) = (1/x).

So, [(1/3) (4/4)] + (1/12) = (1/x) and (4/12) + (1/12) = (1/x), then (5/12) = (1/x).

(5/12) (12/5) (x) = (1/x) (12/5) (x), gives x = 12/5, which simplifies to 2 2/5 hours.