22. 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
I don’t understand this
Wait... no it's 6.15 hours
6.15 hours trust
Well, let me break it down for you. Bob takes 10 hours to shingle the roof on his own, while James takes 16 hours. So if they work together, they'll definitely get it done faster than either of them individually.
Now, imagine Bob and James as a dynamic duo in the world of shingle superheroes. Bob is the "Speedy Shingler," able to lay down shingles at lightning speed. And James is the "Precise Shingler," making sure every shingle is perfectly aligned.
When they put their powers together, it's like a choreographed dance on the roof. Bob's speed complements James's precision, and they can shingle the entire roof in record time.
To find out how long it will take them working together, we need to find their combined shingle-shingling rate. One way to do this is to add up their individual rates.
Bob's rate is 1 roof per 10 hours, and James's rate is 1 roof per 16 hours. So, their combined rate is 1/10 + 1/16 roofs per hour.
To add these fractions, we need a common denominator, which in this case would be 80. So, 1/10 + 1/16 can be simplified to 8/80 + 5/80, which equals 13/80 roofs per hour.
Now, we divide 1 by this combined shingle-shingling rate to find out how many hours it will take them to shingle the roof together.
1 divided by 13/80 is approximately 6.15 hours, rounded to two decimal places.
So, Bob and James will take around 6.15 hours to shingle the roof together.
No worries, I'll be happy to explain it to you!
To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work completed per unit of time. In this case, the work is shingling the roof, and the time is given in hours.
Let's calculate the work rate for each person first. Bob can shingle the roof in 10 hours, so his work rate is 1 roof/10 hours, or 1/10 roofs per hour. Similarly, James can shingle the roof in 16 hours, so his work rate is 1 roof/16 hours, or 1/16 roofs per hour.
Now, when Bob and James work together, their work rates are additive. So, their combined work rate is (1/10 + 1/16) roofs per hour.
To find out how long it will take them to shingle the roof working together, we can invert the combined work rate to get the time required per roof. The combined work rate is (1/10 + 1/16) roofs per hour, which is equal to (16 + 10)/(10*16) roofs per hour, or 26/160 roofs per hour.
Now, we can calculate the time required to shingle one roof by inverting the combined work rate. This is equal to 1 roof / (26/160 roofs per hour), which simplifies to 160/26 hours.
To get the answer in rounded form, we divide 160 by 26 and round it to the nearest hundredth. So, it will take them approximately 6.15 hours to shingle the roof working together.
I hope this explanation helps you understand how to solve the problem!
look at how much of the job each can do in 1 hour
Bob does 1/10 of the job
James does 1/16 of the job.
Together, they can do 1/10 + 1/16 = 13/80 of the roof in one hour
So, it will take them 80/13 = 6 2/13 hours
This is why the solution to such work problems is usually written
1/10 + 1/16 = 1/x