Page 161 - Math Course 2 (Book 2)

Understanding Weighted Averages

Speed of Two Vehicles
Your Turn!
Examples Speed of One Vehicle

RESCUE In the morning, when traffic is light, it takes 30
minutes to get to work. The trip is 15 miles through
A railroad switching operator has discovered towns. In the afternoon, when traffic is a little
that two trains are heading toward each other on heavier, it takes 45 minutes. What is the average
the same track. Currently, the trains are 53 miles speed for the round trip?
apart. One train is traveling at 75 miles per hour
and the other 40 miles per hour. The faster train A. 24 miles per hour
will require 5 miles to stop safely, and the slower B. 30 miles per hour
train will require 3 miles to stop safely. About how C. 15 miles per hour
many minutes does the operator have to warn the D. 45 miles per hour
train engineers to stop their trains?
Answer
Draw a diagram.
53 miles

Takes 5 Takes 3
miles to stop miles to stop

53 – (5 + 3) = 45 miles left

Let m = the number of minutes that the operator
has to warn the train engineers to stop their trains
safely. Make a table. Speed of Two Vehicles
r t d = rt Two students left the school on their bicycles at the

Fast Train 75 m 75m same time, one heading north and the other
heading south. The student heading north travels
Other Train 40 m 40m 15 miles per hour, and the one heading south

Write and solve an equation using the information travels at 17 miles per hour. After about how many
in the table. minutes will they be 7.5 miles apart?

Distance distance
traveled by traveled by
fast train plus other train equals 45 miles. A. 17 minutes
B. 15 minutes
75m + 40m = 45 C. 14 minutes
D. 30 minutes

75m + 40m = 45 Original equation

115m = 45 Simplify.
115m = 45 Divide each side by 115.
115 115 Answer
Round to the nearest
m ≈ 0.39
hundredth.
Convert to minutes by
0.39 x 60 = 23.4
multiplying by 60.
The operator has about 23
Answer
minutes to warn the engineers

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