Algebra 1 Section 7.6

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

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

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.

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.

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.

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

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.

Definition A knot is a unit of speed, referring to nautical miles per hour, that is approximately 1.151 mi/hr. It is often used to measure speeds in aviation and sea navigation.

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

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.

Homework: pp. 310-312