Train A and train B start at the same point and travel in opposite directions.
Train A travels at a constant rate of 80 miles per hour, and train B travels at
a constant rate of 60 miles per hour. If train A starts traveling 2 hours before
train B, how many miles will train A have traveled when the two trains are
720 miles apart?Step 1: Put the given information into the r × t = d table. The rate for trains
A and B are given as 80 miles per hour and 60 miles per hour, respectively.
To solve for the number of miles Train A will have traveled, you need to
determine how many hours Train A traveled. Let t = the number of hours
Train A travels. Since Train A started 2 hours before Train B, and the two
trains stop traveling at the same time, Train B must have traveled t – 2 hours.
Thus in terms of t, Train A’s distance is 80t and Train B’s distance is 60(t –2).
rate (mi/hr) × time (hr) = distance (miles)
↓ ↓ ↓
Train A: 80 × t = 80t
Train B: 60 × t – 2 = 60(t – 2)
As in the previous example, it is essential to identify the relationship between
the two trains’ distances. For the two trains to end up 720 miles apart,
Train A must cover some portion of the 720 miles and Train B must cover
the rest. Thus the sum of their distances is 720. Expressed algebraically, the
equation is:
Train A’s distance + Train B’s distance = 720
↓ ↓ ↓
80 t + 60 (t – 2) = 720Step 2: Now solve for t:
80 t + 60t – 120 = 720
14 0t = 840
t = 6
You are asked to solve for the number of miles Train A traveled, so plug 6 in
for Train A’s time:
rate (mi/hr) × time (hr) = distance (miles)
↓ ↓ ↓
80 × 6 = 80(6)
Train A’s distance is 80 × 6 = 480.342 PART 4 ■ MATH REVIEW04-GRE-Test-2018_313-462.indd 342 12/05/17 12:03 pm