Two airplanes are each traveling at a constant speed.
The table below shows the total number of miles the first airplane traveled as a function of time.
Hour: 2, 3, 4
Total Distance (miles): 320, 480, 640
The equation y=ax represents the total number of miles, y , traveled by the second plane as a function of the numbers of hours, x .
If the second plane is traveling faster, then what must be true about a?
Answers
Answer:
Module 9: Multi-Step Linear Equations
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Using the Distance, Rate, and Time Formula
LEARNING OUTCOMES
Use the problem-solving method to solve problems using the distance, rate, and time formula
One formula you’ll use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant speed. The basic idea is probably already familiar to you. Do you know what distance you traveled if you drove at a steady rate of
60
miles per hour for
2
hours? (This might happen if you use your car’s cruise control while driving on the Interstate.) If you said
120
miles, you already know how to use this formula!
The math to calculate the distance might look like this:
distance
=
(
60
miles
1
hour
)
(
2
hours
)
distance
=
120
miles
In general, the formula relating distance, rate, and time is
distance
=
rate
⋅
time
DISTANCE, RATE, AND TIME
For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula
d
=
r
t
where
d
=
distance,
r
=
rate, and
t
=
time.
Notice that the units we used above for the rate were miles per hour, which we can write as a ratio
m
i
l
e
s
h
o
u
r
. Then when we multiplied by the time, in hours, the common units “hour” divided out. The answer was in miles.
EXAMPLE
Jamal rides his bike at a uniform rate of
12
miles per hour for
3
1
2
hours. How much distance has he traveled?
Solution:
Step 1. Read the problem.
You may want to create a mini-chart to summarize the
information in the problem.
d
=
?
r
=
12
mph
t
=
3
1
2
hours
Step 2. Identify what you are looking for. distance traveled
Step 3. Name. Choose a variable to represent it. let d = distance
Step 4. Translate.
Write the appropriate formula for the situation.
Substitute in the given information.
d
=
r
t
d
=
12
⋅
3
1
2
Step 5. Solve the equation.
d
=
42
miles
Step 6. Check: Does 42 miles make sense?
.
Step 7. Answer the question with a complete sentence.Explanation: i took the test