Question

7.33. Tom can paint Mr. Thatcher's fence in 6 hours, while Huck can paint Mr. Thatcher's fence in 5 hours. If they work together, then how long will it take them to paint the fence?

Answer 1

Answer:

It takes them 30/11 hours to paint them together.

Step-by-step explanation:

This is known as a work problem (rate * time = work). We are given the individual times for Tom and Huck (6 hours and 5 hours respectively). However, we are not given the rates at which they can paint the fence. Since we know that the total work that they both do individually is 1 (there is 1 job to do), we can calculate the rates at which Tom and Huck paint the fence on their own:

$Tom: R_{T}*6=1\\Huck: R_{H}*5=1$

We can isolate R{t} and R{h} to find the rates at which Tom and Huck work:

$Tom: R_{T}=\frac{1}{6}\\Huck: R_{H}=\frac{1}{5}$

Now, we can calculate the time it takes for Tom and Huck to work together using the same formula (the combined rate is just the sum of Tom and Huck's individual rates):

$(\frac{1}{6} +\frac{1}{5})*T=1\\\\T*(11/30)=1 , T = 30/11$

Therefore, the time it takes them to paint the fence together is 30/11 Hours

Answer 2

Answer:

The number of hours it will take them to paint the fence is 2.7 hours.

Step-by-step explanation:

Given:

Tom can paint Mr. Thatcher's fence in 6 hours, while Huck can paint Mr. Thatcher's fence in 5 hours.

Find:

the number of hours it will take them to paint the fence

Step 1 of 1

Determine their work rates, and then add them.

In particular, Tom can paint $\frac{1}{6}$ of a fence per hour, and Huck can paint $\frac{1}{5}$ of a fence per hour.

So, together they can paint $\frac{1}{6}+\frac{1}{5}=\frac{11}{30}$ of a fence per hour. Therefore, the time to paint the whole fence is $\frac{1 \text { fence }}{\frac{11}{30} \text { fences per hour }}=\frac{30}{11}$ hours

$=2 \frac{8}{11} \text { hours, }$ or a little over 2.7 hours.