keith has to grind tha values on his mercedes. he estimates it will take him 8 hrs.. his friends joe and russ have done the samejob in 10 and 12 hrs. respectively. keith had worked for 2 hrs... joe for another half an hour alone and russ came along and together they finished the job. how long did it take them to finish?
Your School Subject is Math.
Also -- is Keith grinding VALVES or VALUES on his car?
To solve this problem, we'll calculate the individual rates of work for each person and then use those rates to find out how long it took them to finish the job when working together.
Let's start by finding the individual rates of work for each person:
- Keith estimated he will take 8 hours to finish the job, so his work rate is 1/8 jobs per hour (1 job divided by 8 hours).
- Joe took 10 hours to finish the job, so his work rate is 1/10 jobs per hour.
- Russ took 12 hours to finish the job, so his work rate is 1/12 jobs per hour.
Next, let's calculate the amount of work done in the time Keith, Joe, and Russ worked individually:
- Keith worked for 2 hours, so he completed 2 * (1/8) = 1/4 of the job.
- Joe worked for another 0.5 hours (30 minutes is equivalent to 0.5 hours), so he completed 0.5 * (1/10) = 1/20 of the job.
- Together, Keith and Joe completed 1/4 + 1/20 = 5/20 + 1/20 = 6/20 = 3/10 of the job.
Since Keith and Joe completed 3/10 of the job together, the remaining work left to be done is 1 - 3/10 = 10/10 - 3/10 = 7/10.
Now, we can find the combined work rate of Keith, Joe, and Russ when they work together:
- The combined work rate is the sum of their individual work rates: 1/8 + 1/10 + 1/12 = 30/240 + 24/240 + 20/240 = 74/240 = 37/120 jobs per hour.
Finally, we can determine the time it took them to finish the remaining work:
- To finish the remaining 7/10 of the job, we divide the amount of work left by the combined work rate: (7/10) / (37/120) = (7/10) * (120/37) = 84/37 hours.
Therefore, it took them approximately 84/37 hours to finish the remaining work together.
Keith did 1/4 of the job is 2 hours. Then Joe did 1/20 of the job in 1/2 hour. By that time, the job is 5/20 or 1/4 done.
When you say "together they finished the job" I will assume that all three of them then finished the job together.
Together, they work at a combined rate
1/8 + 1/10 + 1/12 job/hour = (15+12+10)/120 = 37/120 job/hr
To finish the remaining 3/4 of the job, the time required is
(3/4)/(37/120) = 90/37 = 2.43 hours
If Joe and Russ finished the job together, their rate of work is 22/120 job/hr and the time required is
(3/4)/(22/120) = 90/22 = 4.09 hours