SOLUTION: An airplane passenger, Winston, has a few crates of supplies that he will be bringing with him on his adventure into the Amazon. Having years of experience, the airplane's pilot ca

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Question 1157495: An airplane passenger, Winston, has a few crates of supplies that he will be bringing with him on his adventure into the Amazon. Having years of experience, the airplane's pilot can load his plane by himself in 42 minutes. On the other hand, Winston can load his crates in the plane by himself in 56 minutes. How long will it take both Winston and his pilot to load the crates into the plane working together?
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.

One can make  1%2F42 of the job per minute, working alone.


The other can make  1%2F56 of the job per minute, working alone.


Working together, they can make  1%2F42+%2B+1%2F56 = %2856%2B42%29%2F%2842%2A56%29 = 98%2F%286%2A7%2A7%2A8%29 = %2814%2A7%29%2F%286%2A7%2A7%2A8%29 = 1%2F24 of the job per minute.


It means that they will complete the job in 24 minutes, working together.    ANSWER

Solved.

-------------------

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 josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working
Let +t+ = time in minutes for them to
load the plane working together
-------------------------------------
[ 1 job done ] / [ 42 min ] + [ 1 job done ] / [ 56 min ] = [ 1 job done ] / [ t min ]
+1%2F42+%2B+1%2F56+=+1%2Ft+
Multiply both sides by +168t+
+4t+%2B+3t+=+168+
+7t+=+168+
+t+=+24+
Working together they can load
the plane in 24 min
------------------------------------
check:
+1%2F42+%2B+1%2F56+=+1%2F24+
+.02381+%2B+.017857+=+.041667+
+.041667+=+.041667+
OK