John can clean an attic in 11 hours. DeShawn can clean the same attic in 17 hours. If they worked together how long would it take them? Please solve and show the work. Rounding the answer to the nearest hundredth.

I no the answer is 6.68. I can't remember how to get this.

work with the amount of job done in one hour. In one hour,

John does 1/11
DeShawn does 1/17
together, they do 1/11 + 1/17 = 28/187

so, to do the whole job, they need 187/28 = 6.68

In general, if there are several people taking a,b,c,... hours to do the job, then working together they can do the job in N hours, where

1/N = 1/a + 1/b + 1/c + ...

To solve this question, we need to use the concept of work rates.

First, we'll calculate the work rate of each person. We can do this by taking the reciprocal of the time it takes for each person to complete the task.

John's work rate = 1 job / 11 hours = 1/11 jobs per hour
DeShawn's work rate = 1 job / 17 hours = 1/17 jobs per hour

Next, we'll find the combined work rate when they work together. Since they are working on the same task, their work rates will add up.

Combined work rate = John's work rate + DeShawn's work rate
Combined work rate = 1/11 jobs per hour + 1/17 jobs per hour

To add two fractions, we need a common denominator. In this case, the common denominator is 187. So let's rewrite the fractions with this denominator:

Combined work rate = (17/187) jobs per hour + (11/187) jobs per hour
Combined work rate = (17 + 11) / 187 jobs per hour
Combined work rate = 28 / 187 jobs per hour

Now that we have the combined work rate, we can find the time it takes for them to complete the task by taking the reciprocal:

Time = 1 / Combined work rate
Time = 187 / 28 hours

To round the answer to the nearest hundredth, we divide 187 by 28:

Time = 6.6786 hours

Rounding to the nearest hundredth, the final answer is approximately 6.68 hours.