Rate × Time = Work
Yet in spite of its seeming simplicity, GMAT rate questions are rarely so easy to solve. Instead, GMAT test-makers go to extreme lengths to obfuscate the data provided for each problem, usually by presenting the information in the form of a long and grueling word problem. The onus is on the student to sort out the resulting jumble:
Martin and Wood are hired to perform a copywriting job. Working alone, Martin could finish 2/3 of the the job in 15 days, and if Wood would work alone, he could finish half the job in 9 days. If Martin and Wood work together, how many days would it take them to finish the entire job?
Chances are good that without a systematic approach, you will quickly get bogged down by three common errors:
- Forgetting a vital piece of information: The problem then becomes unsolvable.
- Re-reading the question stem multiple times: This wastes valuable time
- Struggling to retrace your steps: Double-checking your work becomes impossible
Master GMAT’s solution for dealing with chaotic word problems is to organize the information into a table. This technique allows us to approach each problem systematically to reduce careless mistakes and to solve the problem quickly.
Let’s set up one such table which we’ll use for this problem. Label the headers: Rate, Time, and Work:
Before we fill in the rows of the table, let’s use a simple trick to avoid dealing with fractions.
When dealing with rates problems, look to see what the units of work are. Often, if the work is a job or a project, students choose to use the value “1″ for work. The problem with this approach is it that you will end up with lots of messy fractions when calculating the rate and the time. So instead, let’s plug-in a number for the work that will be multiple by all the numbers mentioned in this problem.
This plug-in will contain all the numbers you see in the question stem as factors. We have two fractions in the question stem (2/3 and 1/2) and two integers (15 and 9). A good number, then, be a multiple of all four integers, such as 2·9·15 = 2·135 = 270. So for this problem, we’ll pretend that the job is actually 270 pages of copywriting.
Our next step is to translate each clause in the question stem into a row in our table:
“Working alone, Martin could finish 2/3 of the the job in 15 days“: This corresponds to 2/3 × 270 = 180 for the work, and 15 for the time
“if Wood would work alone, he could finish half the job in 9 days“: Fill in 1/2 × 270 = 135 for the work, and 9 for the time
To calculate the rate for each employee, we simply use the rate-time-work equation. For example, for Martin working alone,
Rate x 15 = 180, so
Rate = 180/15 = 12
Using the same equation, we get a rate of 15 for Wood alone. Use these values to fill in the left-most cell of each row.
“If Martin and Wood work together, how many days would it take them to finish the entire job?” — The combined rate is the sum of the two individual rates, or 27, and the work is 270.
We then look for the amount of time it takes the duo to work together:
27 x Time = 270
Time = 270/27 = 10
The table tactic is all you need to solve any speed or rate problem on the GMAT. To test your understanding, here is a challenging “gap” problem, similar to one you may see on the GMAT. Try it using the table tactic:
Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
- The equation Speed x Time = Distance is analogous to Rate x Time = Work
- Treat the “gap” that is being opened/closed as an object deserving its own row