BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Operating alone at their respective constant rates

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Sat Nov 24, 2012 4:09 am

Operating alone at their respective constant rates

by ritumaheshwari02 » Thu Nov 29, 2012 8:54 am
Operating alone at their respective constant rates, machine A produces 1,000 cans each hour and machine B produces 700 cans each hour. If the two machines together must produce 12,000 cans within a certain 8-hour period, what is the least number of hours that machine A must operate?

A. 4.8
B. 5.2
C. 5.6
D. 6
E. 6.4
Top
Source: — Problem Solving |
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Thu Nov 29, 2012 10:07 am
Location: Columbus, Ohio
GMAT Score:760

by Shoba@ManhattanGMAT » Thu Nov 29, 2012 10:35 am
Classic problem of 2 machines working together. We'll need the basic Work formula (Rate * Time = Work) and also keep in mind that when working together, Rates are additive!

If we want A to operate the least amount of hours, then B is going to have to operate the whole time, so B's share of production in 8 hrs is:

W = R * T
W = 700 cans/hr * 8 hr = 5,600 cans

That means we need machine A to pick up the slack for 12,000 - 5,600 = 6,400 cans.

So how long does A have to operate to make 6,400 cans?

W = R * T
6,400 cans = 1000 cans/hr * T
[spoiler]T = 6.4 hrs
E[/spoiler]


You could also do this in 1 step/1 equation, but maybe it's a bit messier to set up?
W (total) = R(A) * T(A) + R(B) * T(B)
12,000 = 1,000 * T(A) + 700 * 8
Same result, [spoiler]T = 6.4; E[/spoiler]
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Tue Jan 31, 2012 6:50 am
Location: New Delhi
Thanked: 16 times
Followed by:2 members
GMAT Score:760

by nisagl750 » Thu Nov 29, 2012 10:49 pm
ritumaheshwari02 wrote:Operating alone at their respective constant rates, machine A produces 1,000 cans each hour and machine B produces 700 cans each hour. If the two machines together must produce 12,000 cans within a certain 8-hour period, what is the least number of hours that machine A must operate?

A. 4.8
B. 5.2
C. 5.6
D. 6
E. 6.4
Back solve.....

In Which of the following type question....Always start with D/E choice.

Lets select D

in 6 Hrs A will produce 6000 Cans
B can work a max of 8Hrs. So B can produce 8*700=5600 Cans

Total cans produced = 6000+5600 = 11600
Since this is less than 12000
A has to work more...

The only option more than 6Hrs is

E
Top
Post new topic Post Reply
• Page 1 of 1