Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1

SECTION 7.5 Applications of Rational Expressions 405


42.Suppose the following triangles are similar. Find yand the lengths of the two unknown
sides of each triangle.


P

N

M

5 y – 2
4

8 y
3

Q

R

T

3

2 y + 2

2 y

Nurses use proportions to determine the amount of a drug to
administer when the dose is measured in milligrams, but the
drug is packaged in a diluted form in milliliters. (Source:
Hoyles, Celia, Richard Noss, and Stefano Pozzi, “Proportional
Reasoning in Nursing Practice,”Journal for Research in Math-
ematics Education.)For example, to find the number of milli-
liters of fluid needed to administer 300 mgof a drug that
comes packaged as 120 mgin 2 mLof fluid, a nurse sets up the
proportion


,

where x represents the amount to administer in milliliters. Use
this method to find the correct dose for each prescription.


43.120 mg of Amakacine packaged as 100 mg in 2-mL vials


44.1.5 mg of morphine packaged as 20 mg ampules diluted in 10 mL of fluid


Solve each problem. See Examples 6 and 7.


120 mg
2 mL

=


300 mg
x mL

45.Kellen’s boat goes 12 mph. Find the rate
of the current of the river if she can go
6 mi upstream in the same amount of
time she can go 10 mi downstream.


46.Kasey can travel 8 mi upstream in the
same time it takes her to go 12 mi down-
stream. Her boat goes 15 mph in still
water. What is the rate of the current?

Distance Rate Time
Downstream 10
Upstream 612 - x

12 +x

Distance Rate Time
Downstream
Upstream

47.On his drive from Montpelier, Vermont, to Columbia, South Carolina, Victor Samuels
averaged 51 mph. If he had been able to average 60 mph, he would have reached his des-
tination 3 hr earlier. What is the driving distance between Montpelier and Columbia?


48.Kelli Hammer is a college professor who lives in an off-campus apartment. On days when
she rides her bike to campus, she gets to her first class 36 min faster than when she walks.
If her average walking rate is 3 mph and her average biking rate is 12 mph, how far is it
from her apartment to her first class?


49.A plane averaged 500 mph on a trip going east, but only 350 mph on the return trip. The
total flying time in both directions was 8.5 hr. What was the one-way distance?


50.Mary Smith drove from her apartment to her parents’ house on a Saturday morning. She
was able to average 60 mph because traffic was light. However, returning on Sunday
night, she was able to average only 45 mph on the same route. The drive on Sunday took
her 1.5 hr longer than the drive on Saturday. What is the distance between Mary’s apart-
ment and her parents’ house?


51.On the first part of a trip to Carmel traveling on the freeway, Marge averaged 60 mph.
On the rest of the trip, which was 10 mi longer than the first part, she averaged 50 mph.
Find the total distance to Carmel if the second part of the trip took 30 min more than the
first part.

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