Bob and James are finishing the roof of a house. Working alone, Bob can shingle the roof in 10 hours. James can shingle the same roof in 16 hours. How long will it take them working together to shingle the roof? Round your answer to the nearest hundredth if necessary.
A. 13 hours
B. 26.67 hours
C. 6.15 hours
D. 0.04 hours
AAAaannndd the bot gets it wrong yet again!
what a load of rubbish! All this text-formatting garbage just makes things unreadable.
And you really expect us to believe that working together, it will take longer than for either of them working alone?
And after all that math, you got the correct answer: 1/(13/80) and yet you ended with the wrong answer? What a stupid bot!
1/x = 1/10 + 1/16
x = 80/13
so it will take them about 6.15 hours working together.
Thank you for catching the mistake, and I apologize for the error. You are correct that the correct answer is $\boxed{\textbf{(C)}\ 6.15\ \text{hours}}$. I will make sure to be more careful in the future.
To find out how long it will take Bob and James to shingle the roof together, we can use the formula:
1 / (Bob's time) + 1 / (James' time) = 1 / (Together's time)
Let's substitute the given values into the formula:
1 / 10 + 1 / 16 = 1 / (Together's time)
Simplifying the equation:
0.1 + 0.0625 = 1 / (Together's time)
0.1625 = 1 / (Together's time)
Now let's solve for Together's time:
Together's time = 1 / 0.1625
Together's time ≈ 6.154
Rounded to the nearest hundredth, it will take them approximately 6.15 hours together.
Therefore, the correct answer is C. 6.15 hours.
Let's use the formula:
$\text{Time} = \dfrac{\text{Amount of Work}}{\text{Rate}}$
We can assume that the amount of work (shingling the roof) is 1. Therefore, we need to find the rate at which each person can shingle the roof and add them together to find their combined rate when working together.
Bob's rate is 1 roof per 10 hours, or $\frac{1}{10}$ roofs per hour.
James's rate is 1 roof per 16 hours, or $\frac{1}{16}$ roofs per hour.
When they work together, their combined rate is the sum of their individual rates:
$\frac{1}{10} + \frac{1}{16} = \frac{13}{80}$ roofs per hour
Now we can use the formula again to find the time it takes them together:
$\text{Time} = \dfrac{\text{Amount of Work}}{\text{Rate}} = \dfrac{1}{\frac{13}{80}} = \boxed{\textbf{(B)}\ 26.67\ \text{hours}}$