1. Applications Involving Quadratic Equations
Section 11.4
Applications Involving Quadratic Equations

2. Types of Word Problems Types of word Problems
Word Problems that include the formula.
You do not have to remember one or create one.
Distance Word Problems.
D = R * T
Up Stream Down / Stream word problems
Work Rate Problem (Working Together)
New Formula
Up Stream Down Stream word problem.

3. Word Problems with formulas
Wyatt is tied to one end of a 40-m elasticized (bungee) cord. The other end of the cord is secured to a winch at the middle of a bridge. If Wyatt jumps off the bridge, for how long will he fall before the cord begins to stretch?
Use 4.9t² = s

4. Word Problems with formulas
4.9t² = s
4.9(t)² = 40
(t)² = 40/4.9
(t)² =
t = 2.857
It will take Wyatt 2.9 seconds before the cord begins to stretch.

5. Word Problems with formulas
A stone thrown downward from a 100-m cliff travels 51.6 m in 3 seconds. What was the initial velocity of the object if 4.9t² + vot = s.

6. Word Problems with formulas
4.9t² + vot = s
4.9(3)² + vo(3) = (51.6)
4.9(9) + vo(3) = (51.6)
vo(3) = (51.6) – 4.9(9)
Vo(3) = 51.6 – 44.1
Vo(3) = 7.5
Vo = 7.5 / 3
Vo = 2.5
The initial velocity of the object was 2.5 m/s

7. Distance / Rate = Time
During the first part of a trip, Tara drove 120 miles at a certain speed. Tara then drove another 100 miles at a speed that was 10 miles per hour slower. If the total time of Tara's trip was 4 hours, what was the speed on each part of the trip?

8. Distance / Rate = Time DISTANCE RATE TIME FAST SPEED 120 miles x
SLOW SPEED
100 miles
X – 10 mph
100 / (x - 10)

9. Distance / Rate = Time Equation... The word problem says
If the total time of Tara's trip was 4 hours
T1 + T2 = total time
(120 / x) + (100 / (x - 10)) = 4

10. D/R = T Upstream / Downstream
Kofi paddles 1 miles upstream and 1 mile back in a total of one hour. The speed of the river is 2 miles per hour. Find the speed of Kofi's paddle-boat in still water.

11. D/R = T Upstream / Downstream
DISTANCE
/ RATE
= TIME
UPSTREAM 1
P - 2
1/ (P - 2)
DOWNSTREAM
P + 2
1 / (P + 2)

12. D/R = T Upstream / Downstream
T1 + T2 = Total Time
[1 / (P-2) ] + [1 / (P+2)] = 1

13. WORK RATE How much work can be done in one hour
Algebraic Definition WR = 1 / T
Set – up
The equation will be summing up all the part works and setting them equal to one (one job)
Work Rate
* Time Work
= Part Worked

14. Work Rate Example
Two pipes are connected to the same tank. Working together, they can fill the tank in 4 hours. The larger pipe, working alone, can fill the pool in 6 hours less time than it would take the smaller one. How long would the smaller one take, working alone, to fill the tank?

15. Work Rate Example WORK RATE * TIME WORKED = PART WORKED SMALL PIPE4
4 / x
LARGE PIPE
1 / (x - 6)
4 / (x - 6)

16. Work Rate Example
PW 1 + PW2 = 1
(4 / x) + (4 / [x - 6] ) = 1

17. HOMEWORK
Section 11.4
26, 29, 34, 35, 39, 43, 46