McGraw-Hill Education GRE 2019

Combining Rates

In certain work questions, you will be given the individual rates of two or more

elements and will be asked about what happens when they work together.

Working alone at a constant rate, Bob can mow 1 lawn in 3 hours. Working

alone at a constant rate, Jack can mow 1 same-sized lawn in 8 hours. If Bob

and Jack work together but independently at their respective constant rates,

how many hours will it take them to mow half a same-sized lawn?

SOLUTION: Bob’s rate is worktime =^13. Jack’s rate is worktime =^18. To determine how long

it takes them to mow the lawn when they work together, you need their

combined rate. The combined rate is the sum of their individual rates. In this

case, their combined rate is^18 +^13 =^1124. This means that, when they work

together, Bob and Jack can mow^1124 of a lawn in 1 hour. Now input this rate

into the r × t = w formula:

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

↓ ↓ ↓

1124 × t =^12

Note that you input^12 for the total work done, since the question is asking for

the time necessary for them to mow half the lawn.

Solve for t:

(^1124 )t =^12

t = (^12 )(^2411 ) =^1211 hours

CHAPTER 12 ■ FROM WORDS TO ALGEBRA 345

04-GRE-Test-2018_313-462.indd 345 12/05/17 12:04 pm