Concept CheckSolve each problem.
17.Suppose Stephanie walks Dmiles at Rmph in the same time that Wally walks dmiles at
rmph. Give an equation relating D, R, d, and r.
18.If a migrating hawk travels mmph in still air, what is its rate when it flies into a steady
headwind of 6 mph? What is its rate with a tailwind of 6 mph?
Set up the equation you would use to solve each problem. Do not actually solve the equation.
See Example 2.
SECTION 7.7 Applications of Rational Expressions 47319.Mitch Levy flew his airplane 500 mi
against the wind in the same time it took
him to fly 600 mi with the wind. If the
speed of the wind was 10 mph, what was
the rate of his plane in still air? (Let
rate of the plane in still air.)
20.Janet Sturdy can row 4 mph in still
water. She takes as long to row 8 mi
upstream as 24 mi downstream. How
fast is the current? (Let rate of the
current.)x=x=drt
Against the Wind 500
With the Wind 600 x+ 10x- 10drt
Upstream 8
Downstream 24 4 +x4 - xSolve each problem. See Example 2.
21.A boat can go 20 mi against a current in the same time that it can go 60 mi with the cur-
rent. The current is 4 mph. Find the rate of the boat in still water.
22.Vince Grosso can fly his plane 200 mi against the wind in the same time it takes him to fly
300 mi with the wind. The wind blows at 30 mph. Find the rate of his plane in still air.
23.The sanderling is a small shorebird about 6.5 in. long,
with a thin, dark bill and a wide, white wing stripe. If a
sanderling can fly 30 mi with the wind in the same time it
can fly 18 mi against the wind when the wind speed is
8 mph, what is the rate of the bird in still air? (Source:
U.S. Geological Survey.)
24.Airplanes usually fly faster from west to east than from east to west because the prevail-
ing winds go from west to east. The air distance between Chicago and London is about
4000 mi, while the air distance between New York and London is about 3500 mi. If a jet
can fly eastbound from Chicago to London in the same time it can fly westbound from
London to New York in a 35-mph wind, what is the rate of the plane in still air? (Source:
Encyclopaedia Britannica.)
25.An airplane maintaining a constant airspeed takes as long to go 450 mi with the wind as
it does to go 375 mi against the wind. If the wind is blowing at 15 mph, what is the rate of
the plane in still air?
26.A river has a current of 4 km per hr. Find the rate of Jai Singh’s boat in still water if it goes
40 km downstream in the same time that it takes to go 24 km upstream.
27.Connie McNair’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.
28.Howie Sorkin can travel 8 mi upstream in the same time it takes him to go 12 mi down-
stream. His boat goes 15 mph in still water. What is the rate of the current?