SOLUTION: Tammy and Cheryl are building a bridge over a small river. Tammy can do the job alone in 24 hours. Cheryl can do the job alone in 28 hours. Tammy worked on the project alone 4 hour

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Tammy and Cheryl are building a bridge over a small river. Tammy can do the job alone in 24 hours. Cheryl can do the job alone in 28 hours. Tammy worked on the project alone 4 hour      Log On


   

Question 992308: Tammy and Cheryl are building a bridge over a small river. Tammy can do the job alone in 24 hours. Cheryl can do the job alone in 28 hours. Tammy worked on the project alone 4 hours before Cheryl joined her. The two then finished the job together. How long did it take the two to finish the job that Tammy had started alone.
Found 2 solutions by Theo, josmiceli:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Tammy can do the job in 24 hours.
her rate is therefore 1/24 of the job in one hour.

Cheryl can do the job in 28 hours.
her rate is therefore 1/28 of the job in one hour.

this is because rate * time = quantity.

quantity is equal to 1 because they are building 1 bridge.

for Tammy, this equation becomes rate * 24 = 1 which gets rate = 1/24.
for Cheryl, this equation becomes rate * 28 = 1 which gets rate = 1/28.

Tammy works alone for 4 hours.

at a rate of 1/24 of the bridge in 1 hour, she completes 4/24 of the bridge in 4 hours.


this leaves 20/24 of the bridge remaining to be completed.

working together, their rates are additive, so you get:

(1/24 + 1/28) * time = 20/24

simplfy this to get 1/24 * time + 1/28 * time = 20/24.

multiply both sides of the equation by 24 * 28 to get:

28 * time + 24 * time = 20/24 * 24 * 28

combine like terms on the left and simplify on the right to get:

52 * time = 20 * 28

divide both sides of this equation by 52 and solve for time to get:

time = (20 * 28) / 52.

simplify this fraction to get:

time = (5 * 28) / 13

this simplifies further to get:

time = 140 / 13 hours.

that's equivalent to 10 and 10/13 hours.

the decimal equivalent of that would be time = 10.7692307692... hours.

fractional form is an exact answer.
decimal form is an approximaton.

4/24 of the job that Tammy finished alone and 20/24 of the job that Tammy and Cheryl finished together took 4 hours plus 10 and 10/13 hours for a total of 14 and 10/13 hours.







Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What fraction of the job did Tammy get
done in 4 hrs?
[ fraction of job ] = [ her rate of working ] x [ hrs worked ]
+%28+1%2F24+%29%2A4+=+1%2F6+
That means there is +5%2F6+ of the job left to do
when Cheryl joined her
------------------------
Add their rates of working to get their
rate working together
Let +t+ = time ime hrs for the both of them
to do +5%2F6+ of the job
+1%2F24+%2B+1%2F28+=+%28%28+5%2F6+%29%29%2Ft+
Multiply both sides by +2+
+1%2F12+%2B+1%2F14+=+%28%28+5%2F3+%29%29%2Ft+
Multiply both sides by +84t+
+7t+%2B+6t+=+140+
+13t+=+140+
+t+=10.77+
It takes them 10.77 hrs to finish the job working together
------------------
check:
+1%2F24+%2B+1%2F28+=+%28%28+5%2F6+%29%29%2Ft+
+1%2F24+%2B+1%2F28+=+%28%28+5%2F6+%29%29%2F10.77+
+1%2F24+%2B+1%2F28+=+5%2F64%2C62+
+.041667+%2B+.035714+=+.077375+
+.077381+=+.077375+
error due to rounding off, I think
Recheck my math