1. Algebra 1
Section 7.6

2. Motion Problems As we saw in Chapter 3, the basic formula is rt = d.
Subscripted variables are sometimes used in problems like these.

3. Example 1 r t d rf 6 6rf rs 6 6rs rf = rs + 2 6rf + 6rs = 612 rf = 52
Faster car rf 6
6rf
Slower car rs 6
6rs
rf = rs + 2
6rf + 6rs = 612
rf = 52
rs = 50

4. Example 1
r t d
Faster car rf 6
6rf
Slower car rs 6
6rs
The slower car is traveling at 50 mi/hr, and the faster car is traveling at 52 mi/hr.

5. Wind and Water A headwind of x mi/hr reduces the rate of speed by x.
A tailwind of x mi/hr increases the rate of speed by x.

6. Wind and Water
A current of x mi/hr increases the downstream rate of speed (compared to the rate in still water) by x.
A current of x mi/hr decreases the upstream rate of speed by x.

7. Example 2 r t d b + c 3 12 b – c 2 4 3(b + c) = 12 2(b – c) = 4 b = 3
Downstream
b + c 3 12
Upstream
b – c 2 4
3(b + c) = 12
2(b – c) = 4
b = 3
c = 1

8. Example 2
r t d
Downstream
b + c 3 12
Upstream
b – c 2 4
Brent’s paddling rate is 3 mi/hr and the rate of the current is 1 mi/hr.

9. Definition
A knot is a unit of speed, referring to nautical miles per hour, that is approximately mi/hr.
It is often used to measure speeds in aviation and sea navigation.

10. Example 3 r t d p – w 4 1900 p + w 3.5 1900 4(p – w) = 1900
Flight to CA
p – w 4
1900
Flight Home
p + w
3.5
1900
4(p – w) = 1900
3.5(p + w) = 1900
p ≈ 509
w ≈ 34

11. Example 3
r t d
Flight to CA
p – w 4
1900
Flight Home
p + w
3.5
1900
The airplane’s rate of speed is about 509 knots, and the wind speed is about 34 knots.

12. Homework: pp