GMAT question - Labeling machine A working alone takes 1 minute to p... - Review

Type: Problem Solving

Difficulty: 3 star rating

Labeling machine A working alone takes 1 minute to put labels on 100 cans and labeling machines A and B working together take 45 seconds to put labels on 100 cans. How long would it take machine B working alone to put labels on 100 cans?

  1. 25 seconds
  2. 1 minute 45 seconds
  3. 2 minutes
  4. 2 minutes 30 seconds
  5. 3 minutes

Explanation

We have been given some of the times in the question in minutes and some in seconds.

It is important to make sure that when we are working out the answer that we don't confuse our units so lets convert all the information into seconds.

The question tells us

  • Machine A alone takes 60 seconds
  • Machines A and B together take 45 seconds

And asks us to find the length of time that machine B will take alone.

Use the formula

Putting this information into the general formula for solving combined work rate problems we get

\[\frac{1}{60} + \frac{1}{B} = \frac{1}{45}\]

Where B is the time machine B takes to label 100 cans working on its own. Solving this equation for B will give us the answer to this question.

Solve for B

Firstly we put all the fractions one one side of the equation

\[\frac{1}{B} = \frac{1}{45} - \frac{1}{60}\]

Put both fractions in terms of their lowest common denominator.

\[\frac{1}{B} = \frac{4}{180} - \frac{3}{180}\]

Subtract the fractions

\[\frac{1}{B} = \frac{1}{180}\]

Invert both sides of the equation

\[B = 180 \text{ seconds }\]

Convert to minutes

All the answers are expressed in minutes so we need to convert this answer to minutes. There are 60 seconds in a minute so

\[B = 180 \text{ seconds } = \frac{180}{60} \text{ minutes } = 3 \text{ minutes }\]

Therefor the answer is E.

Comments (1):

  1. Let's look at one more logical way of finishing this quickly.

    Given A alone takes 60 seconds
    A and B together takes 45 seconds.

    Form these two statements we can conclude that, from the second statement even though A did not work for 15 seconds, the work is completed because B has done it in 45 seconds.

    So if A takes 15 seconds for a work, B takes 45 seconds.

    Since for the entire work A takes 1 minute, B takes 3 minutes

    Sureshbala on 11 Mar 2009 (permalink)

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