College Algebra 9th txtbk

96 CHAPTER 1 EQUATIONS AND INEQUALITIES
per hour. The planes carry radios with a maximum range of
500 miles. When (to the nearest minute) will these planes no longer
be able to communicate with each other?
94. AIR SEARCH If the second plane in Problem 93 leaves at
6:30 A.M. instead of 6 A.M., when (to the nearest minute) will the
planes lose communication with each other?
95. ENGINEERING One pipe can fill a tank in 5 hours less than another.
Together they can fill the tank in 5 hours. How long would it
take each alone to fill the tank? Compute the answer to two decimal
places.
96. ENGINEERING Two gears rotate so that one completes 1 more
revolution per minute than the other. If it takes the smaller gear
1
1 second less than the larger gear to complete 5 revolution, how
many revolutions does each gear make in 1 minute?
97. PHYSICS—ENGINEERING For a car traveling at a speed of
v miles per hour, under the best possible conditions the shortest
distance d necessary to stop it (including reaction time) is given by
the formula d 0.044v 2 1.1v, where d is measured in feet.
Estimate the speed of a car that requires 165 feet to stop in an
emergency.
98. PHYSICS—ENGINEERING If a projectile is shot vertically into
the air (from the ground) with an initial velocity of 176 feet per second,
its distance y (in feet) above the ground t seconds after it is shot
is given by y 176t 16t 2 (neglecting air resistance).
(A) Find the times when y is 0, and interpret the results physically.
(B) Find the times when the projectile is 16 feet off the ground.
Compute answers to two decimal places.
99. ARCHITECTURE A developer wants to erect a rectangular building
on a triangular-shaped piece of property that is 200 feet wide
and 400 feet long (see the figure).
(B) A potential buyer for the building needs to have a floor area of
25,000 square feet. Can the builder accommodate them?
100. ARCHITECTURE An architect is designing a small A-frame
cottage for a resort area. A cross section of the cottage is an isosceles
triangle with an area of 98 square feet. The front wall of the cottage
must accommodate a sliding door that is 6 feet wide and 8 feet
high (see the figure). Find the width and height of the cross section
of the cottage. [Recall: The area of a triangle with base b and altitude
h is bh2.]
6 feet
8 feet
101. TRANSPORTATION A delivery truck leaves a warehouse and
travels north to factory A. From factory A the truck travels east to
factory B and then returns directly to the warehouse (see the figure).
The driver recorded the truck’s odometer reading at the warehouse
at both the beginning and the end of the trip and also at factory B,
but forgot to record it at factory A (see the table). The driver does
recall that it was farther from the warehouse to factory A than it was
from factory A to factory B. Since delivery charges are based on
distance from the warehouse, the driver needs to know how far factory
A is from the warehouse. Find this distance.
200 feet
REBEKAH DRIVE
Property
A
l
Proposed
Building
w
Property Line
Factory A
Factory B
FIRST STREET
400 feet
(A) Building codes require that industrial buildings on lots that size
have a floor area of at least 15,000 square feet. Find the dimensions
that will yield the smallest building that meets code. [Hint: Use
Euclid’s theorem* to find a relationship between the length and
width of the building.]
*Euclid’s theorem: If two triangles are similar, their corresponding
sides are proportional:
a
b
c
a
b
c
a
a¿ b b¿ c c¿
Warehouse
Odometer readings
Warehouse 5 2 8 4 6
Factory A 5 2 ? ? ?
Factory B 5 2 9 3 7
Warehouse 5 3 0 0 2