George takes 8 hrs to copy a 50-page book. Sonya can copy the same book in 6 hrs. How many hours would it take them to copy a 100-page manucript, if they work together?
2007-03-30 08:08:15 · 5 answers · asked by Rjoy 1 in Education & Reference ➔ Homework Help
Both of the first two answerers were correct though they each took a different approach to achieve their answers.
6.87 Hours = 6 6/7 Hours
2007-03-30 08:40:26 · answer #1 · answered by B Scott 4 · 1⤊ 0⤋
George takes 4/3 as much time as Sonya to do copy the same amount. That means that he works 3/4 as fast as her.
If given the same amount of time, the ratio of the amount of pages George has copied to Sonya is 3 to 4. That means that given seven pages together, George will do 3 and Sonya will do 4. 100/7= 14 and 2/7. In order to scale from 7 to 100 pages, you multiply 3 and 4 respectively by 14 2/7.
George does 42 6/7 pages, and Sonya does 57 1/7. George and Sonya took the same amount of time.
We know that it took Sonya 6 hours to copy 50 pages. This time, she copied 57 1/7 pages, which is 8/7 as much. (1/7 of 50 is 7 1/7). That would take her 8/7 as many hours as well. 8/7 of 6 is 48/7 or 6 6/7 hours.
2007-03-30 15:31:54 · answer #2 · answered by Eddie Mishaan 2 · 0⤊ 0⤋
George copies 50/8 pages per hour.
Sonya copies 50/6 pages per hour.
Working together, they copy (50/8 + 50/6)
= 25(1/4 + 1/3) pages per hour.
To copy 100 pages therefore takes them:
100/ ( 25(1/4 + 1/3) ) hr
= 4 / ( 1/4 + 1/3 ) hr
= 4 / ( 7 / 12) hr
= 48/7 hr
= 6 6/7 hr.
2007-03-30 18:04:51 · answer #3 · answered by Anonymous · 0⤊ 0⤋
This is not as complicated as it seems. You can figure out their individual rates and add them together, since they will be working together. Then just divide that total into the number of pages they have to copy, in this case, 100.
George's rate = 50 pages / 8 hours = 6 1/4 pages / hour
Sonya's rate = 50 pages / 6 hours = 8 1/3 pages / hour
Now add them together:
(25/4) + (25/3) = (75 + 100) / 12 = 175/12 pages / hour.
Since they have 100 pages to copy, just divide 100 by their total work rate, 175/12, to find out how long it will take both working together to copy them.
T = 100 / (175/12) = 1200/175 â 6.857
So, it would take them roughly 6 hours 51 minutes and 26 seconds (0.857 hours is about 51 minutes and 26 seconds) working together to copy the manuscript.
You might also observe there is another way of solving this problem. You can also divide their combined work rate into 50 (the original number of pages) to find T and then multiply that figure by 2, since 100 is 2 x 50.
2007-03-30 16:10:39 · answer #4 · answered by MathBioMajor 7 · 0⤊ 0⤋
George copies 50/8 = 6.25 pages per hour.
Sonya copies 50/6 = 8.33 pages per hour.
Together, they copy 14.55 pages per hour.
100 pages would take 100/14.55 = 6.87 hours
2007-03-30 15:26:00 · answer #5 · answered by falconrf 4 · 0⤊ 0⤋