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Quadratic Equation Word Problems

Learn how to solve various types of word problems involving quadratic equations, such as distance, work rate, and downstream/upstream problems. Includes relevant formulas.

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Quadratic Equation Word Problems

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  1. Applications Involving Quadratic Equations Section 11.4

  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 = 8.1632653 • 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

  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

  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)

  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

  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

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