Problem Solving

This can be solved by a long method, but any shorter way under time constraint ?

what is the Official Answer? Is it a ? 7?

yea, it is A.

Can you please explain ?

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..

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.

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

the work formula actually makes this hard and MegaMehta made an awesome approach to this question.

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.