Intermediate Algebra (11th edition)

Concept Check The formula (distance rate time) is used in the applications in
Exercises 27–30.To prepare to use this formula, work Exercises 25 and 26.

25.If the rate of a boat in still water is 10 mph,
and the rate of the current of a river is
xmph, what is the rate of the boat
(a)going upstream (that is, against the
current, which slows the boat down);
(b)going downstream (that is, with the
current, which speeds the boat up)?

26.If the rate of a killer whale is 25 mph and the whale swims for yhours, give an expression
for the number of miles the whale travels.

Solve each problem. See Example 4.

27.A train travels 150 km in the same time that a plane covers
400 km. If the rate of the plane is 20 km per hr less than
3 times the rate of the train, find both rates.

28.A freight train and an express train leave towns 390 km
apart, traveling toward one another. The freight train
travels 30 km per hr slower than the express train. They
pass one another 3 hr later. What are their rates?

d=rt = *

SECTION 4.3 Applications of Systems of Linear Equations 243

21.A party mix is made by adding nuts that sell for $2.50 per kg to a cereal mixture that sells
for $1 per kg. How much of each should be added to get 30 kg of a mix that will sell for
$1.70 per kg?

Number of Price per

Kilograms Kilogram Value

Nuts x 2.50

Cereal y 1.00

Mixture 1.70

Liters of Percent (as Liters of

Drink a decimal) Pure Juice

50% Juice x 0.50

30% Juice y 0.30

Mixture 0.45

23.A total of $3000 is invested, part at 2%
simple interest and part at 4%. If the
total annual return from the two invest-
ments is $100, how much is invested at
each rate?

24.An investor will invest a total of

$15,000 in two accounts, one paying 4%

annual simple interest and the other 3%.

If he wants to earn $550 annual interest,

how much should he invest at each rate?

Rate

Principal (as a decimal) Interest

x 0.02 0.02x

y 0.04 0.04y

3000 100

Rate

Principal (as a decimal) Interest

x 0.04

y 0.03

15,000

Upstream

(against

the current)

Downstream

(with the

current)

rt d

Train x 150

Plane y 400

rtd

Freight Train x 3

Express Train y 3

22.A fruit drink is made by mixing fruit juices. Such a drink with 50% juice is to be mixed
with another drink that is 30% juice to get 200 L of a drink that is 45% juice. How much
of each should be used?