"It Would Take One Machine 4 Hours To Complete a Large Production Order..." — GMAT® Worked Solution
From Episode 44 of Real GMAT® Problems (The GMAT® Strategy Podcast). For the strategy behind the rate chart, read: GMAT® Work/Rate Problems: Why Organization Matters.
The Problem
Source: Official Guide for GMAT® Review, 11th Edition
It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
(A) 7/12
(B) 1 1/2
(C) 1 5/7
(D) 3 1/2
(E) 7
Try it before reading on.
Setting Up the Rate Chart
You see the word "rates." Make the chart.
Three columns: Rate × Time = Work. One row per machine.
Fill in what the problem gives you:
| Rate | × Time | = Work | |
|---|---|---|---|
| Machine 1 | ? | 4 hours | 1 order |
| Machine 2 | ? | 3 hours | 1 order |
Solving for Each Rate
What times 4 equals 1? That's 1/4.
Machine 1's rate: 1/4 orders per hour.
What times 3 equals 1? That's 1/3.
Machine 2's rate: 1/3 orders per hour.
| Rate | × Time | = Work | |
|---|---|---|---|
| Machine 1 | 1/4 orders per hour | 4 hours | 1 order |
| Machine 2 | 1/3 orders per hour | 3 hours | 1 order |
Combining the Rates
Two machines working together — add their rates.
If one robot builds 4 cars per hour and another builds 7 per hour, together they build 11. Same idea with fractions.
1/4 + 1/3 = 3/12 + 4/12 = 7/12 orders per hour
| Rate | × Time | = Work | |
|---|---|---|---|
| Machine 1 | 1/4 orders per hour | 4 hours | 1 order |
| Machine 2 | 1/3 orders per hour | 3 hours | 1 order |
| Together | 7/12 orders per hour | ? | 1 order |
Finding the Time
7/12 orders per hour × how many hours = 1 order?
12/7 hours. That's 1 and 5/7 hours.
The answer is (C).
Why This Problem Matters
About 12% of test takers pick (A) — 7/12. That's the rate, not the time.
They did every step right. They found the rates. They added them. They got 7/12. Then they picked 7/12 as their answer.
The answer choices include both the rate and the time. The chart prevents this mix-up. You look at the column and you know what the number is.
Ready for the next one? It adds variables and multiple scenarios for the same machine: Two Machines, Y and Z — Variables and Multiple Rows.
Want the full strategy? Read: GMAT® Work/Rate Problems: Why Organization Matters
From Episode 44 of Real GMAT® Problems (The GMAT® Strategy Podcast).