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

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) (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) (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 ]

That means there is of the job left to do
when Cheryl joined her
------------------------
Add their rates of working to get their
rate working together
Let = time ime hrs for the both of them
to do of the job

Multiply both sides by

Multiply both sides by

It takes them 10.77 hrs to finish the job working together
------------------
check:

error due to rounding off, I think
Recheck my math
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