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Distance & Motion Problems
d=rt formuladistance chart
Copyright © 2013 by Lynda Aguirre 1
Distance Formula
Copyright © 2013 by Lynda Aguirre 2
d = r t
distance = rate x time
(how far) = (how fast, speed) x (how long it takes)
Section A: One object traveling in one direction
Copyright © 2013 by Lynda Aguirre 3
Section A: One object traveling in one direction
Distance Formula
a. A bird flies at a speed of 8 mph for 2 hours. How far did the bird travel?
One object moving: Distance Formula: d = r t (distance = rate x time)
d = (8)(2)
d= 16 miles
What information is given? Speed (this is the rate), r = 8 mph
Travel time, t = 2 hoursDistance? = unknown(How far means we
don’t know the distance)
Copyright © 2013 by Lynda Aguirre 4
Section A: One object traveling in one direction
Distance Formula
b. If a bird flies at a speed of 10 mph, how long would it take for the bird to travel a distance of 30 miles?
One object moving: Distance Formula: d = r t (distance = rate x time)
30 = (10)t
t = 3 hours
What information is given?
Speed (this is the rate), r = 10 mph Travel time, (how long=unknown time)
Distance, d=30 miles
Copyright © 2013 by Lynda Aguirre 5
Section A: One object traveling in one direction
Distance Formula
c. If a bird flies 17 miles in 3 hours, what was its speed?
One object moving: Distance Formula: d = r t (distance = rate x time)
17 = r(3)
r = 5.7 mph
What information is given?
Speed , r = unknownTravel time, t=3 hours
Distance, d=17 miles
17 = 3r
Round off to one decimal placer = 5.66…
Rearrange: Number comes first
Copyright © 2013 by Lynda Aguirre 6
Time Conversion ProblemsWhen calculating distance problems, you will often run into a situationwhere the time has to be converted from decimal form into the more
commonly used hour/minute format.
The next example demonstrates this process
Copyright © 2013 by Lynda Aguirre 7
Section A: One object traveling in one direction
Distance Formula
b. If a bird flies at a speed of 10 mph, how long would it take for the bird to travel a distance of 12 miles?
One object moving: Distance Formula: d = r t (distance = rate x time)
12 = (10)t
t = 1.2 hours
What information is given?
Speed (this is the rate), r = 10 mph Travel time, (how long=unknown time)
Distance, d=12 miles
Convert to hours and minutes
Copyright © 2013 by Lynda Aguirre 8
t = 1.2 hours
Time Conversion Problems
Time conversion: 60 minutes in an hour
.2 x 60 = 12 minutes
The hours are given by the number to the left of the decimal
The minutes must be changed from .2 hours into minutes
t = 1 hour 12 minutes
Copyright © 2013 by Lynda Aguirre 9
Practice Problems
1) A bird flies 18 miles in 3 hours. How fast was the bird traveling?
2) A bird flies at a speed of 8 miles per hour for 6 hours. How far did the bird travel?
3) A bird flies 25 miles in 5 hours. How fast was the bird flying?
4) A bird flies at a speed of 6 miles per hour and travels 37 miles. How long did the trip take?
Use the distance formula to solve the following problems. ConvertUse the distance formula to solve the following problems. Convertyour answers into standard units when necessary.your answers into standard units when necessary.
