SOLUTION: Patty takes two hours to ice a cake alone, whereas Bob takes three hours to ice a cake alone. The number of hours it would take Patty and Bob working together to ice a cake is a

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Question 1201379: Patty takes two hours to ice a cake alone, whereas Bob takes three hours to ice a cake alone. The number of hours it would take Patty and Bob working together to ice a cake is
a) 1 1/5 b) 1 1/4 c) 1 1/3 d) 2 1/2 e) 5
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
P makes  1%2F2  of the job per hour.

B makes  1%2F3  of the job per hour.


Working together, they make  1%2F2+%2B+1%2F3 = 5%2F6  of the job per hour.


Hence, they complete the job in  6%2F5  hours = 1 1%2F5  hours = 1 hour and 12 minutes (option a), working together.

Solved.

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It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Let's say the cake's surface area is 60 square inches.
I picked a value that is a common multiple between 2 and 3 (since 2*3 = 6).
It turns out that the surface area doesn't matter since we'll get the same answer for other surface area values.
Feel free to pick some other positive number.

Patty takes 2 hours to cover 60 square inches when working alone.
Her rate is 60/2 = 30 sq in per hour.
The formula I used is:
rate = (amount done)/(time)

Bob takes 3 hours to cover 60 square inches when working alone.
His rate is 60/3 = 20 sq in per hour.

Their combined rate is 30+20 = 50 sq in per hour.

If the two team up, and don't get in each other's way, then their combined rate is 50 sq in per hour.

Let's determine how long they take when working together.
rate = (amount done)/(time)
rate*time = amount done
time = (amount done)/(rate)
time = (60 sq in)/(50 sq in per hr)
time = (60/50) hr
time = (6/5) hr
time = ( (5+1)/5 ) hr
time = ( 5/5 + 1/5 ) hr
time = ( 1 + 1/5 ) hr

Side notes:
1 hr + 1/5 hr = 1 hr + 0.2 hr = 1.2 hr
or
1 hr + 1/5 hr = 60 min + (1/5)*(60) min = 60 min + 12 min = 72 min
or
1 hr + 1/5 hr = 1 hr + 12 min

Answer: Choice A) 1 1/5
This is the mixed number 1 & 1/5
whole part = 1
fractional part = 1/5