Case Study IV A motorboat whose speed in still water is 24km/hr, takes 1 hour more to go 32 km upstream than to return downstream to the same spot . Based on this information answer the following questions 1\. What is the speed of the motorboat in going upstream, if speed of the stream is x km/hr? 1. (x − 24) km/hr 2. (24 − x) km/hr 3. (x + 24) km/hr 4. none of these 2\. The quadratic equation which represents the given information is: 1. x² − 64x − 576 = 0 2. x² + 64x + 576 = 0 3. x² + 64x − 576 = 0 4. x² − 64x + 576 = 0 3\. Speed of the motorboat in going downstream is: 1. 16 km/hr 2. 8 km/hr 3. 28 km/hr 4. 32 km/hr 4\. Time taken by the motorboat to go 272 km downstream is: 1. 8½ hours 2. 17 hours 3. 12½ hours 4. 6½ hours 5\. Time taken by the motorboat to go 80 km upstream and then to return back to the same spot is: 1. 5½ hours 2. 6½ hours 3. 7½ hours 4. 8½ hours

Question

KnowledgeBoat · Accepted Answer

1\. Given, The speed of the motorboat in still water is 24 km/hr The speed of the stream be x km/hr The speed of the motorboat in going upstream = boat speed in still water − stream speed = (24 - x) km/hr Hence, option (2) is the correct option. 2\. The speed of the motorboat in going downstream = boat speed in still water + stream speed = (24 + x) km/hr Distance to be covered by motorboat = 32km Time = In first case: Time taken by motorboat in going upstream = In second case: Time taken by motorboat in going downstream = The difference in time taken between first case and second case = 1 hour more Hence, option (3) is the correct option. 3\. Solving equation from question 2, ⇒ x2 + 64x - 576 = 0 ⇒ x2 - 8x + 72x - 576 = 0 ⇒ x(x - 8) + 72(x - 8) = 0 ⇒ (x + 72)(x - 8) = 0 ⇒ (x + 72) = 0 or (x - 8) = 0 [Using zero-product rule] ⇒ x = -72 or x = 8 ⇒ x = 8km/hr [speed of the stream cannot be negative] Speed of the motorboat downstream = 24 + x = 24 + 8 = 32 km/hr. Hence, option (4) is the correct option. 4\. The downstream speed of motorboat is 32 km/hr (from Question 3). The time taken by the motorboat to go 272 km downstream = = 8.5 hours Hence, option (1) is the correct option. 5\. Speed of the motorboat upstream = 16 km/hr The time taken by the motorboat to go 80 km upstream = = 5 hours The time taken by the motorboat to return 80 km downstreamstream = = 2.5 hours Total time = 5 + 2.5 = 7.5 hours Hence, option (3) is the correct option.

Mathematics

Quadratic Equations

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