Unit 1 – Number Sense and Algebraic Thinking
Lesson 4 – Evaluating Expressions
Black – Evaluating Expressions
1. A train, whose speed is 75 mph, takes. 3 minutes to pass a car that is going 60 mph in
the same direction. How long is the train?
2. Warren is riding his bike at 15 mph on a road adjacent to race tracks. A train
traveling at 90 mph in the opposite direction at Warren, takes 20 seconds to pass
him. How long is the train?
3. In a recent 50-yard Olympic swimming event, the 1st place finisher beat the 2nd place
finisher by 1/100 of a second. If the winning time was 26.80 seconds, how many
inches behind was the 2nd place finisher when the race ended? (Round to the nearest
inch.)
4. Carolyn drove from her home to school at 40 mph and was 10 minutes late. The next
day she drove to school at 60 mph and was 10 minutes early. How far is Carolyn's
school from her home?
5. In a recent running of the 100-yard dash, the winner-won the race with a time of
9.87 seconds. The 2nd place finisher had a time of 9.92 seconds. When the winner
crossed the finish line, how far behind was the 2nd place finisher?
(Give your answer in yards.)
6. Susan rode her bike alongside a train that was traveling at a speed of 24 mph. If she
was traveling at a speed of 12 mph and it took the train 2 minutes 24 seconds to,
pass her, what is the length of the train?
Solutions
1. ¾ mile
Change the 3 minutes to hours: 3/60 or 3 ÷ 60 = .05 hours
Distance train travels in 3 minutes: Distance = 75 mph x .05 hours
Distance =3.75 miles
Distance car travels in 3 minutes: Distance = 60 mph x .05 hours
Distance = 3 miles
The length of the train is the extra distance the train had to go to pass the car:
3.75 miles - 3 miles = .75 miles
2. 7/12 mile
Change 20 seconds to hours: 20 seconds ÷ 3600 seconds in an hour = .005555 hours
Pretend Warren was standing still. The distance the train traveled in those 20
seconds is: Distance = 90 mph x .005555 hours
Distance = .5 miles
Warren is not standing still, but riding in the opposite direction as the train. He is
therefore making the train pass him more quickly than if he is standing still.
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Unit 1 – Number Sense and Algebraic Thinking
Lesson 4 – Evaluating Expressions
The distance Warren traveled must be added to the train's length.
Warren's distance = 15 mph x .005555 hours.
Distance = .08333
Train's distance traveled ÷ Warren's distance traveled = 7/12 mile
or 1/12 mile
3. One inch
The second place finisher must have had a time of 26.81 seconds in the 50 yard race.
We must first find the speed of the second place finisher in inches per second.
Change yards into inches: 50 x 36 =1800 inches.
Speed in inches per second: 1800 ÷ 26.81 = 67.14 inches per second.
Now we must find out how far the second place swimmer swam when the 1800 inch
race ended at 26.80 seconds.
Distance = 67.14 inches per second x 26.80 seconds
Distance =1799.35 inches
Second place finisher was less than 1 inch from the finish line when the 1800 inch
race ended.
4. 40 miles
Time it took to get to school at 60 mph will be called: t hours
The time it took to get to school at 40 mph was 20 minutes or 1/3 hour longer than
at 60 mph so it will be called: t + 1/3 hours
60 mph trip equation:
40 mph trip equation:
Distance = 60 mph x t
Distance = 40 mph x (t + 1/3)
Distance = 60t
Distance = 40t + 40/3
Because the distances are equal, we can set them equal to each other:
60t = 40t + 40/3
20t = 40/3
t = 2/3 hour
Now that we know the time: Distance to school= 60 mph x 2/3 hour
Distance = 40 miles
5. ½ yard
What is the speed of the second place finisher in yards per second?
100 yards ÷ 9.92 seconds = 10.08 yards per second.
What distance had the second place finisher traveled when the winner crossed the
finish line at 9.87 seconds? (Distance = Speed x Time)
Distance = 10.08 yards per second x 9.87 second
Distance = 99.49 yards
The second place finisher was 100 yards – 99.49 yards = ½ yard behind the winner
when the race ended.
6. .48 miles
Change 2 minutes 24 seconds into hours: 144 second ÷ 3600 = .04 hours
Distance train traveled: Distance = 24 mph x .04 hours
Distance = .96 miles
Distance Susan traveled: Distance = 12 mph x .04 hours
Distance = .48 miles
Because Susan is traveling with the train, her distance must be subtracted from the
distance that the train traveled.
Train’s distance – Susan’s distance = .48
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Unit 1 – Number Sense and Algebraic Thinking
Lesson 4 – Evaluating Expressions
Bibliography Information
Teachers attempted to cite the sources for the problems included in this problem set. In some cases,
sources may not have been known.
Problems
Bibliography Information
1–6
Zaccaro, Edward. Challenge Math (Second
Edition): Hickory Grove Press, 2005.
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