Algebra 1 Common Core Student Edition, Grade 8-9

v d Got It? 2. The zoo has two o th er w ater tanks th at are leaking. O ne tan k contains

10 gal of w ater a n d is leaking at a co n stan t rate of 2 gal/h. The second tank

contains 6 gal of w ater a n d is leaking at a co n stan t rate of 4 g al/h. W hen will

th e tanks have th e sam e a m o u n t of water? Explain.

W hen a p lan e travels from w est to east across the U nited States, th e steady w est-to-east

w inds act as tailwinds. This increases th e p la n e ’s sp eed relative to th e ground. W hen a

plan e travels from east to west, th e w inds act as headw inds. This decreases th e plane's

speed relative to th e ground.

From W est to East

air sp eed + w ind speed = g ro u n d speed

I-----------a----------►j — w—H

I-----------g----------H

From East to W est

air speed — w ind speed = g round speed

Pr o b l em 3 ]

w— f. — g------ 1

So l v i n g a W i n d o r Cu r r e n t Pr o b l e m

Travel A traveler flies from Charlotte, North Carolina, to Los Angeles, California. At

the same time, another traveler flies from Los Angeles to Charlotte. The air speed of

each plane is the same. The ground speeds are shown below. What is the air speed?

What is the wind speed?

Los A n g e le s, CA

Gr o u n d sp eed = 5 5 0 m i / h

Air speed = a

How are the speeds
related?
The a ir speed is a plane's
speed w ith no w in d. A dd
wind speed and air speed
to get the ground speed
w ith a ta ilw in d. S ubtract
wind speed from air
speed to find the ground
speed w ith a h e a d w in d.

Use th e ground speed w ith th e tailw ind an d w ith th e h ead w in d to write th e system.

Let a = th e air speed of th e p lanes. Let w = th e w ind speed.

air w ind _ g round speed

speed speed with tailwind

air

speed

a + w = 550 a

Choose a m eth o d to solve th e system. Use elim ination.

a + w = 550

a — w = 495

2a + 0 = 1045 Add the equations.

a = 522.5 Solve for a.

Substitute 522.5 for a in either eq u a tio n an d solve for w.

522.5 + w = 550 Substitute 522.5 for a in the first equation.

w = 27.5 Solve for w.

The air speed is 522.5 m i / h. The w ind sp ee d is 27.5 m i / h.

w ind _ g round speed

speed with headwind

— w — 495

G

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