Question

Sanjay and Felipe are putting together a 500-piece puzzle. Sanjay could do the entire puzzle by himself in 6 hours, while it would take Felipe 8 hours to do the puzzle alone.
Use the table to write and solve an equation to determine the approximate amount of time it would take Sanjay and Felipe to do the puzzle if they were working together.
0.8 hours
1.7 hours
3.4 hours
7 hours

Answer 1

Answer: the answer is 3.4 hours

Answer 2

What is the time it takes Sanjay to complete the puzzle? 6 hours

What is the time it takes Felipe to complete the puzzle? 8 hours

We can use the general formula of rate and time to solve this problem. Generally we have,

Rate * Time = Work/Job

** where Work/Job for this problem is 1 since they are doing 1 work, which is solving a puzzle

• Finding rate of Sanjay:

$R(6)=1\\R=\frac{1}{6}$

• Finding rate of Felipe:

$R(8)=1\\R=\frac{1}{8}$

Working together, their rate is the sum,

Total Rate = $\frac{1}{6} + \frac{1}{8} = \frac{7}{24}$.

Using the general formula again, we can find the time it will take to solve the puzzle when both works together.

$(\frac{7}{24})T=1\\ T=\frac{1}{\frac{7}{24}}= \frac{24}{7} = 3.43$ hours

Rounding the answer, we have 3.4 hours.

ANSWER: 3.4 hours