SOLUTION: 6. Lysa takes 8 hours to do a job that her sister can do in 7 hours. If Lysa works 1 hour and 20 minutes before her sister joins her, how long will it take the two of them working

Question 75718: 6. Lysa takes 8 hours to do a job that her sister can do in 7 hours. If Lysa works 1 hour and 20 minutes before her sister joins her, how long will it take the two of them working together to finish the job?
7.Togehter, two pipes can fill a vat in 4 h ours. If the larger pipe takes 6 hours to fill the vat, how long does it take the smaller pipe to fill the vat?
8. Stanley and Tom work together at the bank and can put a certain set of data into the computer in 4 hours and 48 minutes. It takes Tom 8 hours to do this work alone. How long does it take Stanley to do this job alone?
9.Lucy can do a job in 4 hours that Caroline takes 3 hours to do. Hazel can also do the same job in 4 hours. How long will it take the three of them working together to do the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
6. Lysa takes 8 hours to do a job that her sister can do in 7 hours. If Lysa works 1 hour and 20 minutes before her sister joins her, how long will it take the two of them working together to finish the job?
:
Let's convert everything to minutes: 8*60=480 min. 7*60=420 min. 1 hr 20m = 80 min
:
Let t = time working together. Let the completed job = 1
:
If L works 80 min she will have completed 80/480 of the job
:
L alone + 2 together = completed job
+ + = 1
:
Multiply each term by (480)(420) and you have:
80(420) + 420t + 480t = (480)(420)
:
33600 + 900t = 201600
:
900t = 201600 - 33600
:
900t = 168000
:
t = 168000/900
:
t = 186.67 min or 3 hrs 6 min 40 sec
:
Check using hrs. 186.67 min = 3.11 hrs, 1 hr 20 min = 1.33 hr
1.33/8 + 3.11/8 + 3.11/7 =
.16625 + .38875 + .44428 = .99928 not 1 because of the those fractional hrs.
:
:
7.Together, two pipes can fill a vat in 4 h ours. If the larger pipe takes 6 hours to fill the vat, how long does it take the smaller pipe to fill the vat?
:
The same mixture equation is used. Let x = time to fill with the small pipe
Let the completed job = 1
+ = 1
:
Multiply by 6x and you have:
4x + 6(4) = 6x
24 = 6x - 4x
2x = 24
x = 12 hr small pipe by itself:
:
Check: 4/6 + 4/12 = 1
:
:
8. Stanley and Tom work together at the bank and can put a certain set of data into the computer in 4 hours and 48 minutes. It takes Tom 8 hours to do this work alone. How long does it take Stanley to do this job alone?
:
Same as above; change 4 hr 48 min to hrs. 4 + 48/60 = 4.8 hrs
+ = 1
:
See if you can do this one, exactly like the previous problem
:
:
9.Lucy can do a job in 4 hours that Caroline takes 3 hours to do. Hazel can also do the same job in 4 hours. How long will it take the three of them working together to do the job?
:
Let t = time for all three to complete the job (1)
+ + = 1
:
Multiply thru by 12 to get rid of the denominators, you then have:
3t + 4t + 3t = 12
:
10t = 12
:
t = 12/10
:
t = 1.2 hrs or 1 hr + .2(60) = 1 hr 12 min
:
Check:
1.2/4 + 1.2/3 + 1.2/4 =
.3 + .4 + .3 = 1
:
How about this? Did it make sense to you? Any questions?
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