Respuesta :
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:
[tex]Tom: R_{T}*6=1\\Huck: R_{H}*5=1[/tex]
We can isolate R{t} and R{h} to find the rates at which Tom and Huck work:
[tex]Tom: R_{T}=\frac{1}{6}\\Huck: R_{H}=\frac{1}{5}[/tex]
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):
[tex](\frac{1}{6} +\frac{1}{5})*T=1\\\\T*(11/30)=1 , T = 30/11[/tex]
Therefore, the time it takes them to paint the fence together is 30/11 Hours
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 [tex]$\frac{1}{6}$[/tex] of a fence per hour, and Huck can paint [tex]$\frac{1}{5}$[/tex] of a fence per hour.
So, together they can paint [tex]$\frac{1}{6}+\frac{1}{5}=\frac{11}{30}$[/tex] of a fence per hour. Therefore, the time to paint the whole fence is [tex]$\frac{1 \text { fence }}{\frac{11}{30} \text { fences per hour }}=\frac{30}{11}$[/tex] hours
[tex]$=2 \frac{8}{11} \text { hours, }$[/tex] or a little over 2.7 hours.
