Step 2: Once you have done so, you can plug the values into the formula:
rate (mi/hr) × time (hr) = distance (miles)
↓ ↓ ↓5 × 13 = (^53)
Multiple Rates
For distance questions, the r × t = d table is particularly useful for problems that
involve multiple rates or multiple travelers. In these situations, you will generally
want to create two rows on the r × t = d table, fill them in with the appropriate
values or variables, and use the resulting expressions to identify a relationship
between the distances.
Bob and Jack start at opposite ends of a 200-mile track. Bob travels at a
constant rate of 50 miles per hour and Jack travels at a constant rate of 75
miles per hour. If they start traveling toward each other at the same time, in
how many hours will they meet?
Step 1: Put the given information into the r × t = d table:
rate (mi/hr) × time (hr) = distance (miles)
↓ ↓ ↓
Bob: 50 × t = 50 t
Jack: 75 × t = 75 t
Note that there are two rows—one for Jack and one for Bob. You are asked
to solve for the amount of time they travel, so let t represent time. Since Bob
and Jack start and end at the same time, they will each have traveled for t
hours. In terms of t, Bob travels 50t miles and Jack travels 75t miles.
Now you must identify the relationship between these distances. Since they
are traveling toward each other, Bob will travel some of the 200 miles and
Jack will travel the remaining distance. Thus the distances the two travel
must add up to 200. Algebraically, you can represent this relationship as:
Bob’s distance + Jack’s distance = 200
↓ ↓ ↓
50 t + 75 t = 200
Step 2: Solve for t:
125 t = 200
t =^85 hour
CHAPTER 12 ■ FROM WORDS TO ALGEBRA 341
04-GRE-Test-2018_313-462.indd 341 12/05/17 12:03 pm