SOLUTION: A man can do a job in 10 hours and his younger son can do it in 12 hours. After the father and his younger son have been working for 1 hour, the older son joins them, and the three

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A man can do a job in 10 hours and his younger son can do it in 12 hours. After the father and his younger son have been working for 1 hour, the older son joins them, and the three      Log On


   

Question 1101866: A man can do a job in 10 hours and his younger son can do it in 12 hours. After the father and his younger son have been working for 1 hour, the older son joins them, and the three completed the job in 3 more hours. How long will it take the older son to do the job?
Found 3 solutions by josmiceli, greenestamps, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Man's rate is:
[ 1 job ] / [ 10 hrs ]
Younger son's rate is:
[ 1 job ] / [ 12 hrs ]
Let older son's rate =
[ 1 job ] / [ t hrs ]
----------------------
Let +x+ = the fraction of the
job man and younger son get done
in 1 hr
Add their rates to get rate working together
+1%2F10+%2B+1%2F12+=+x%2F1+
Multiply both sides by +60+
+6+%2B+5+=+60x+
+60x+=+11+
+x+=+11%2F60+ is the fraction that gets done.
There is +49%2F60+ of the job left to do
------------------------------------------
+1%2F10+%2B+1%2F12+%2B+1%2Ft+=+%28%28+49%2F60+%29%29%2F3+
+1%2F10+%2B+1%2F12+%2B+1%2Ft+=+49%2F180+
Multiply both sides by +180t+
+18t+%2B+15t+%2B+180+=+49t+
+33t+%2B+180+=+49t+
+16t+=+180+
+t+=+11.25+
Working alone, the older son
can do the job is 11 hrs 15 min
------------------------------
Get another opinion if needed

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor's answer is right.

Here is my solution, by a slightly different method that looks easier than what they did.

As the other tutor showed in her calculations, the man and the younger son can do 11/60 of the job in 1 hour.

When the older son joins them, the job is finished in another 3 hours.

That means the man and his younger son work for 4 hours, and the older son works for 3.

Since the man and the younger son do 11/60 of the job in 1 hour, they do 44/60 of the job in 4 hours.

That means the older son does 16/60 of the job in 3 hours, which means 16/180 of the job in 1 hour.

So the number of hours the older son alone would need to do the job alone is 180/16 = 11.25 hours.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Father and young son work together 1 hour.
Father, young son, and older son all work together 3 hours.

x, time for older son to do ONE job, working alone


%281%2F10%2B1%2F12%29%2A1%2B%281%2F10%2B1%2F12%2B1%2Fx%29%2A3=1
Simplify and solve for x.