Lindsey and Stephen work at a factory. Lindsey can complete one full job in three hours, and Stephen can complete the same job in five hours. If Lindsey and Stephen work together on the job for one hour, then how long, in minutes, will it take Stephen to finish the job himself?
L --- 1/3 job/hr
S ---1/5 job/hr
together 1/3 + 1/5 = 8/15 job/hr
(8/15 j/h)(1 h) = 8/15 job done
that leaves (15-8)/15 = 7/15 to do
(1/5)job/hr * t = 7/15 job
t = 35/15 hr for S to finish
35/15 hr * 60 min/hr = 140 min
Well, it seems like Lindsey and Stephen make quite the dynamic duo! If Lindsey can complete the job in three hours and Stephen in five, then together they complete 1/3 of the job in one hour, and Stephen does 1/5 of the job in that same time.
So, after working together for one hour, there's 1/3 + 1/5 = 8/15 of the job left to be done. Since Stephen can finish 1/5 of the job in one hour, we can divide the remaining work by his rate: (8/15) / (1/5) = 8/3 hours.
Now, to convert this to minutes, we know that there are 60 minutes in an hour. So 8/3 hours is equal to (8/3) * 60 = 160 minutes.
Therefore, it will take Stephen approximately 160 minutes to finish the job himself.
To find out how long it will take Stephen to finish the job himself after working with Lindsey for one hour, we need to find out how much of the job is completed in one hour by both of them working together. The combined job completion rate can be calculated by adding the individual rates.
Lindsey's job completion rate = 1 job / 3 hours = 1/3 job per hour
Stephen's job completion rate = 1 job / 5 hours = 1/5 job per hour
Their combined job completion rate = (1/3 + 1/5) job per hour
By simplifying the fractions and adding them, we get:
(5 + 3) / 15 = 8/15 job per hour
So, when Lindsey and Stephen work together, they can complete 8/15 of the job in one hour.
Now, to find out how long it will take Stephen to finish the remaining part of the job, we need to subtract the part completed by both from one whole job:
Remaining job = 1 - (8/15) = 7/15 job
Stephen's job completion rate = 1/5 job per hour
To find the time it will take Stephen to finish the remaining job, divide the remaining job by Stephen's rate:
Time = Remaining job / Stephen's rate = (7/15) / (1/5)
Dividing fractions can be done by multiplying by the reciprocal:
Time = (7/15) * (5/1) = (7 * 5) / (15 * 1) = 35/15
Converting to minutes:
1 hour = 60 minutes
So, (35/15) * 60 = 140 minutes
Therefore, it will take Stephen 140 minutes to finish the job himself after working with Lindsey for one hour.
To solve this problem, we first need to determine how much of the job Lindsey and Stephen can complete together in one hour.
You can find this by adding their rates of work. Lindsey completes one full job in three hours, so her rate of work is 1 job / 3 hours or 1/3 of a job per hour. Similarly, Stephen completes one full job in five hours, so his rate of work is 1 job / 5 hours or 1/5 of a job per hour.
To find their combined rate of work, we add their individual rates: 1/3 + 1/5 = 8/15. That means together, Lindsey and Stephen can complete 8/15 of a job in one hour.
Now, we want to know how long it will take Stephen to finish the job by himself. We already know that Lindsey and Stephen's combined rate is 8/15 of a job per hour.
To find Stephen's rate, we subtract Lindsey's rate from the combined rate: 8/15 - 1/3 = 8/15 - 5/15 = 3/15 = 1/5.
This means Stephen can complete 1/5 of a job in one hour.
Since Stephen can complete 1/5 of a job in one hour, it will take him 5 hours to complete the entire job by himself.
To convert this to minutes, we multiply the number of hours by 60 (since there are 60 minutes in an hour): 5 hours * 60 minutes/hour = 300 minutes.
Therefore, it will take Stephen 300 minutes to finish the job by himself.