February 13, 2013
Lesson 7.7
Applications With Rational
Expressions, Including Variation
Work Problems
A person's rate of work multiplied by the time at work
equals the amount of work completed by that person.
When two people are working together, the work
completed by one person added to the work completed
by the other person equal the total work completed.
Joe can paint the outside of a house in 6 days working alone. His helper,
Frank, can paint the outside of the same house in 9 days working alone.
How long will it take to paint the outside of the house working together?
If Joe takes 6 days to paint the house, his rate is 1/6 of
the house per day. What is Frank's rate?
How long will it take them to paint the house?
Categories
Rate
Time
work done
Since they are just painting the house once, we add the
work done by each of the painters and set it equal to 1.
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February 13, 2013
We have already used the distance formula
to solve certain motion problems.
What are two other forms of this formula?
and
A plane travels 1200 miles against the jet stream, causing its airspeed to be
decreased by 20 mph. On the return flight, the plane travels with the jet
stream so that its airspeed is increased by 20 mph. If the total flight time of
the round trip is six and one-third hours, what is the plane's rate in still air?
Categories
Distance
Rate
Time
Against JS
1200
r - 20
1200
r - 20
With JS
1200
r + 20
1200
r + 20
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February 13, 2013
Two variables y and x vary directly if y = kx. If y
varies directly as the nth power of x, then y = kxn,
where k is the constant of variation.
Solving Variation Problems
1. Write the equation.
2. Substitute the initial values and find k.
3. Substitute for k in the equation found in step 1.
4. Substitute the additional data into the equation from
step 3 and solve for the unknown.
Examples
Suppose y varies directly as x. If y = 27 when x = 63,
find y when x = 91.
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February 13, 2013
Page 554 #32
According to Ohm's law, the current, I, which is measured
in amperes, in an electrical circuit varies directly with the
voltage, V. If the current is 0.64 amperes when the voltage is 24 volts, find the current when the voltage is 48 volts.
The distance a free-falling body falls is directly proportional to the square of the time it has been falling.
Page 555 #36
On the Moon, an object falls 14.58 meters in 3 seconds.
How long will it take for the object to fall 58.32 meters?
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February 13, 2013
Two variables y and x vary inversely if
. If
varies inversely as the nth power of x, where
k is the constant of variation.
Examples
Suppose p varies inversely as q. If p is 8 when q is
3.25, what is q when p is 2?
The length of a radio wave varies inversely with its frequency.
Page 556 #48
If the frequency of a radio wave is 800 kilohertz when the
wavelength is 200 meters, find the frequency when the
wavelength is 500 meters.
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February 13, 2013
Two variables y and x vary inversely if
. If
varies inversely as the nth power of x, where
k is the constant of variation.
Examples
Suppose p varies inversely as q. If p is 8 when q is
3.25, what is q when p is 2?
The length of a radio wave varies inversely with its frequency.
Page 556 #48
If the frequency of a radio wave is 800 kilohertz when the
wavelength is 200 meters, find the frequency when the
wavelength is 500 meters.
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February 13, 2013
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