McGraw-Hill Education GRE 2019

Work Problems: Rate × Time = Work

The second type of rate problem involves work. In contrast to distance problems,

work problems are concerned with some output per unit of time. An output can

be something produced (such as widgets, cups, cars, etc.) or a job done (such as

mowing a lawn, cooking a meal, writing a paper, etc.). In both cases, you want to

use the work formula, though as you will see, the way you express work will differ.

Let’s look at a simple work question:

If a machine produces pencils at a constant rate of 1,500 pencils per hour, in

how many hours will the machine have produced 6,750 pencils?

SOLUTION: Put the given values into the rate × time = work (RTW) table. The

machine’s rate is 1,500 pencils/hour, and its output (work) is 6,750 pencils.

Since you are trying to solve for time, assign a variable: t

rate (pencils/hr) × time (hr) = work (pencils)

↓ ↓ ↓

1,500 × t = 6,750

Solve for t:

1,500t = 6,750

t = 6,7501,500 = 4.5

Let’s look at another example, this time with work represented as some job done

instead of units produced:

Working at a constant rate, Bob can mow 3 same-sized lawns in 5 hours.

How many hours will it take Bob to mow 2 same-sized lawns?

SOLUTION: Set up the RTW table. Remember that rate = worktime , so Bob’s rate will

be lawnshour =^35.

rate (lawns/hr) × time (hr) = work (lawns)

↓ ↓ ↓

35 × t = 2

Solve for t:

35 t = 2

t = 2(^53 ) =^103 hours

344 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 344 12/05/17 12:04 pm