Case Study II A bus travels at a certain average speed for a distance of 75 km and then it travels a distance of 90 km at an average speed of 10 km/hr more than the original speed. If it takes 3 hours to complete the total journey, then based on this information, answer the following questions: 1\. If the original speed of the bus be x km/hr, then time taken by the bus to travel the next given distance is: 1. 75/x hours 2. 90/x hours 3. (90/(x + 10)) hours 4. (90/(x − 10)) hours 2\. The quadratic equation for the given information, if the original speed of the bus be x km/hr, is: 1. x² + 45x − 250 = 0 2. x² − 45x − 250 = 0 3. x² − 75x − 450 = 0 4. x² − 45x + 250 = 0 3\. The original speed of the bus is: 1. 50 km/hr 2. 40 km/hr 3. 75 km/hr 4. 60 km/hr 4\. The speed of the bus during which it travels the distance of 90 km is: 1. 70 km/hr 2. 50 km/hr 3. 60 km/hr 4. 85 km/hr 5\. The time taken by the bus to travel a distance of 510 km with the new speed is: 1. 8 hours 2. 8½ hours 3. 10¹/₅ hours 4. 12¾ hours

Question

KnowledgeBoat · Accepted Answer

1\. Given, Original speed of the bus = x km/hr Next given distance = 90 Speed for next distance = (x + 10) km/hr Time = Time taken for next distance = . Hence, option (3) is the correct option. 2\. Time taken by bus to travel 75 km = Time taken by bus to travel 90 km = Given, Total time taken to complete the journey = 3 hours Hence, option (2) is the correct option. 3\. Solving, ⇒ x2 - 45x - 250 = 0 ⇒ x2 + 5x - 50x - 250 = 0 ⇒ x(x + 5) - 50(x + 5) = 0 ⇒ (x + 5)(x - 50) = 0 ⇒ (x + 5) = 0 or (x - 50) = 0 [Using zero-product rule] ⇒ x = -5 or x = 50 ⇒ x = 50 [As speed cannot be negative] Speed = 50 km/hr Hence, option (1) is the correct option. 4\. The new speed of bus = x + 10 = 50 + 10 = 60 km/hr. Hence, option (3) is the correct option. 5\. Given, Distance = 510 km New speed = 60 km/hr. Time = = hrs. Hence, option (2) is the correct option.

Mathematics

Quadratic Equations

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