Precalculus
HS Mathematics
Unit: 03 Lesson: 02
Conversions with Dimensional Analysis KEY
26 in
Sample: 40 mph is how many feet per second?
40 mi
5280 ft
1 hr
1 min



1 hr
1 mi
60 min
60 sec
=
40(5280) ft
60(60) sec
2
3
= 58
ft/sec
Start with the given information as a ratio. Then cancel unwanted units by multiplying by various
forms of “1” (comparing unit equivalents, such as 1 mi = 5280 ft).
1)
A car went 44 feet through an intersection in only 0.5 seconds. How fast was the car going in
miles per hour?
44 ft
0.5 sec

60 sec
1 min
60
min


1 hr
5,280 ft
2)
In football, Drew runs a 40-yard dash in 5.1 seconds. Describe his rate in miles per hour.
Around 16 miles per hour
3)
A leaky faucet in our kitchen wastes a cup of water every 10 minutes.
How fast is this water leaking in gallons per day?
9 gallons per day
4)
With my internet connection, my computer estimated that it would take 18
seconds to download an 890-KB file. What is the transfer rate in gigabytes
(GB) per day?
©2012, TESCCC
07/24/12
1 gal = 4 qt
1 qt = 4 cups
1 MB = 1024 KB
1 GB = 1024 MB
page 1 of 3
Precalculus
HS Mathematics
Unit: 03 Lesson: 02
About 4 GB/day
5)
33 31
An old-fashioned record player spins an album at a rate of
rpm
(revolutions per minute). Convert this rate into degrees per second.
200/sec
©2012, TESCCC
07/24/12
1 rev = 360
page 2 of 3
Precalculus
HS Mathematics
Unit: 03 Lesson: 02
Conversions with Dimensional Analysis KEY
6)
The world record for the fastest spinning on ice skates is 1848 of rotation
per second. Describe this rate in revolutions per minute.
308 revolutions per minute
7)
On average, the earth is 93 million miles away from the center of
the sun.
A) Assuming that the earth’s orbit is circular, estimate the
number of miles our planet travels in one complete
revolution around the sun.
1 revolution = 2r  584,336,234 miles
B)
8)
1 rev = 360
Earth
Sun
93 million
miles
The complete revolution around the sun takes 1 year. How
fast is the earth moving in this orbit in feet per second?
584,336,233 miles per year  97,834 feet per second
Suppose a car wheel is 26 inches in diameter.
A) If the tire completes one rotation, how far would the car travel?
1 rotation = 1 revolution = 2r  81.68 inches
B)
If the car is traveling at 60 miles per hour, how fast is the car
wheel spinning in revolutions per second?
60 mi
1 hr
©2012, TESCCC

5280
ft

1 mi
12 in
1 ft
07/24/12

1 rev
81.68 in

60 min
1 hr

60 sec
page 3 of 3