This can be solved by a long method, but any shorter way under time constraint ?
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GMAC Practice Exam PS question
Source: Beat The GMAT — Problem Solving |
Harvesting machine H harvested 40 acres of wheat in 8 hours
so it harvested 40/8= 5 acres in one hour.
then the machine K was brought in. Together they harvested the rest in 5 hours. so 100-40=60 acres in 5 hours. So together they harvested in 12 hours.
So machine K's rate was 12 hours together-5hours H's rate= 7 hours.
Note: I suppose that when they both worked together, the time taken did not decrease like in other work problems which is why we didn't take the usual 1/5+1/x=1/12..
so it harvested 40/8= 5 acres in one hour.
then the machine K was brought in. Together they harvested the rest in 5 hours. so 100-40=60 acres in 5 hours. So together they harvested in 12 hours.
So machine K's rate was 12 hours together-5hours H's rate= 7 hours.
Note: I suppose that when they both worked together, the time taken did not decrease like in other work problems which is why we didn't take the usual 1/5+1/x=1/12..
Thanks, I got it now. I took the usual 1/x+1/5 like we do for each of the work problems. But the key is 1/5 is work done in 1 hour.
Thanks Megha.
Thanks Megha.
Hi,
Though the answer is 7 acres per hr. I believe the approach is this.
First information H completing 40 acres in 8 hrs is used in finding out H's speed i.e 5 acres per hour.
In the second set of information H and K together finished the work in 5 hrs
We know that had H worked alone, he would have completed 60 acres in 12 hrs.
so
1/5 = 1/12 + 1/K gives you k's time ie 60/7 hrs and hence K's speed is 60/60/7 ie 7 acres per hour
Though the answer is 7 acres per hr. I believe the approach is this.
First information H completing 40 acres in 8 hrs is used in finding out H's speed i.e 5 acres per hour.
In the second set of information H and K together finished the work in 5 hrs
We know that had H worked alone, he would have completed 60 acres in 12 hrs.
so
1/5 = 1/12 + 1/K gives you k's time ie 60/7 hrs and hence K's speed is 60/60/7 ie 7 acres per hour
the work formula actually makes this hard and MegaMehta made an awesome approach to this question.
Appetite for 700 and I scraped my plate!
I solved it this way, may ad another view, but logic is similar to earlier posts:
1) K harvested 40 acres, so there is (100-40=) 60 acres left.
2) Rate of K is 40/8 = 5 acres/hr
3) Its given that 5hrs is needed for K & H to harvest the rest (=60 acres)
4) with 2) H needed to harvest (60-25=) 35 acres in 5hrs, hence H needed 7hrs.
Good luck,
Joe.
1) K harvested 40 acres, so there is (100-40=) 60 acres left.
2) Rate of K is 40/8 = 5 acres/hr
3) Its given that 5hrs is needed for K & H to harvest the rest (=60 acres)
4) with 2) H needed to harvest (60-25=) 35 acres in 5hrs, hence H needed 7hrs.
Good luck,
Joe.
