Solve each problem by using two variables. See Examples 1 – 4.
244 CHAPTER 4 Systems of Linear Equations
rtd
Upstream 2
Downstream x+y
x-y
29.In his motorboat, Bill Ruhberg travels
upstream at top speed to his favorite
fishing spot, a distance of 36 mi, in 2 hr.
Returning, he finds that the trip down-
stream, still at top speed, takes only 1.5 hr.
Find the rate of Bill’s boat and the rate
of the current. Let the rate of the
boat and the rate of the current.
30.Traveling for 3 hr into a steady head
wind, a plane flies 1650 mi. The pilot
determines that flying with the same
wind for 2 hr, he could make a trip of
1300 mi. Find the rate of the plane and
the wind speed.
y=
x=
x – y mph
into wind
x + y mph
with wind
31.(See the Chapter Introduction.) How
many pounds of candy that sells for
$0.75 per lb must be mixed with candy
that sells for $1.25 per lb to obtain 9 lb
of a mixture that should sell for $0.96
per lb?
32.The top-grossing tour on the North
American concert circuit for 2009 was
U2, followed in second place by Bruce
Springsteen and the E Street Band.
Together, they took in $217.5 million
from ticket sales. If Springsteen took in
$28.5 million less than U2, how much did
each band generate? (Source:Pollstar.)
33.Tickets to a production of A Midsummer Night’s Dreamat Broward College cost $5 for
general admission or $4 with a student ID. If 184 people paid to see a performance and
$812 was collected, how many of each type of ticket were sold?
34.At a business meeting at Panera Bread, the bill for two cappuccinos and three house lattes
was $14.55. At another table, the bill for one cappuccino and two house lattes was $8.77.
How much did each type of beverage cost? (Source:Panera Bread menu.)
35.The mixed price of 9 citrons and 7 fragrant wood apples is 107; again, the mixed price of
7 citrons and 9 fragrant wood apples is 101. O you arithmetician, tell me quickly the price
of a citron and the price of a wood apple here, having distinctly separated those prices
well. (Source:Hindu work, A.D. 850.)
36.Braving blizzard conditions on the planet Hoth, Luke Skywalker sets out in his snow
speeder for a rebel base 4800 mi away. He travels into a steady head wind and makes the
trip in 3 hr. Returning, he finds that the trip back, now with a tailwind, takes only 2 hr. Find
the rate of Luke’s snow speeder and the speed of the wind.
rtd
Into Head Wind
With Tailwind
