Algebra II Pre AP
Name
Worksheet 8.1 & 8.6 Applications
Date
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Period.
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More Direct, Inverse and Joint Variation
1.
Find x when y
= 1000,
if y varies directly as x and y
= 50 when
= 200.
x
'K == J/I) (JO
=
= 36, find
=
2.
If P varies inversely as the square root of q, and p
3.
If s varies directly as r and inversely as t, and s = 10 when r = 5 and t = 3, for what value of twill
4.
If
5.
If w is inversely proportional
6.
Suppose that z varies jointly as u and v and inversely as w, and that
when u = 3, v = 10 and w = 5.
12 when q
p when q
16.
s = 3 when r = 4?
z is inversely proportional to rand z = 32 when r = 1.5, find r when z = 8.
to the square of
v, and w
= 3 when
v = 6, find w when v = 3.
z = 0.8 when u = 8, v = 6 and w = 5. Find z
t- == 0.5
7.
The heat loss through a glass window varies jointly as the area of the window and the difference between the
inside and outside temperatures.
If the loss through a window with area 3 m2 is 720 BTU when the temperature
difference is 15° C, what is the heat loss through a window with area 4.5 m2 when the temperature difference is
12°(7
8.
When air is pumped into an automobile tire, the pressure required varies inversely as the volume. If the
pressure is 80 pounds when the volume is 140 cubic inches, find the pressure when the volume is 100 cubic
inches.
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9.
By one of Kepler's laws (proved by Newton), the square of the period of a satellite in circular orbit is directly
proportional to the cube of the radius of the orbit. A satellite in orbit 9600 km above the surface of the Earth
has period 5.6 h. How high is a satellite in a "stationary" orbit that has period 24 h? (Use 6400 km as the radius
of Earth.)
10. A sprocket gear 8 in. in diameter is connected to a gear 3 in. in diameter.
when the larger one rotates at 216 r/min (revolutions per minute)?
Ifthe smaller gear is attached to the 28-inch-diameter
(Hint: r/min * circumference of gear = k)
How fast does the smaller gear rotate
rear wheel of a bicycle, how fast does the wheel rotate?
Application - Work
For each of the fol/owing
define the variables write a rational equation and solve.
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11. Jennifer can mow the lawn in 20 min. Kristen can mow the lawn in 30 min. If they work together,
how long will
it take them to mow the lawn?
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12. Mark can wash the car in 30 min. Zach can wash the car in 40 min. Working together, can they wash the car in
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13. Kendall, by herself, can paint our house in 12 days. If Meghan helps, it will only take 4 days to paint the house.
How long would it take Meghan by herself?
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14. If one hose fills a pool in 4 hours, a second hose fills it in 2 hours and a third hose in 5 hours, how long will it take
to fill the pool with all three hoses turned on?
15. Lindsey can clean the house in 8 h by herself. After working alone for 2 h, Brooke comes over to help. They
work for 2 hours together and finish cleaning. How long would it have taken Brooke, alone, to clean the house?
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16. A large pipe can fill a tank in 5 h and a smaller pipe can fill it in 8 h. A third pipe can empty the tank in 10 h. How
long would it take to fill the tank with all three pipes open and working?
17. Crane A can unload the container ship in 10 hours and Crane B can unload it in 14 hours. Crane A started to
unload the ship at noon and was joined by Crane B at 2 p.m. At what time was the unloading job of the ship
completed?
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18. Jim can stuff 500 envelopes in an hour and a half. It takes Michael SO minutes to stuff the same number of
envelopes. How long will it take Jim and Michael working together to stuff 1000 envelopes?
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19. The county's new asphalt paving machine can surface 1 km of highway in 10 hours. A much older machine can
surface 1 km in 18 hours. How long will it take them to surface 21 km of highway if they start at opposite ends
and work day and night?
20. Pipes A and B can fill a storage tank in 8 hours and 12 hours, respectively. With the tank empty, pipe A was
turned on at noon, and then pipe B was turned on at 1:30 p.m. At what time was the tank full?
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