Question

a bus travel at a certain average speed for a distance of 75 km and then travel a distance of 90 km at an average speed of 10 km/h more than the first speed if it takes 3 hours to complete the total journey find its first speed.

Answer 1

if it takes 3 hour to complete the whole journey and the distance is respectively 75 and 90
total speed = total distance/ total time
= 75+90/3 = 165/3
= 55 km/ hr
let first speed is x
then second speed is x+10 ( because second speed is 10km/hr more than first speed)
x+x+10=55
2x=55-10
x= 45/2=22.5
first speed is22.5 km per hour

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the original speed of the bus be x km/h.

Time taken to cover 75 km = 75/x hrs

New speed = x + 10 km/h

Time taken to cover 90 km with new speed = 90/x + 10 hrs

According to the Question,

⇒ 75/x + 90/(x + 10) = 3

⇒ 75(x + 10) + 90x/x(x + 10) = 3

⇒ 165x + 750 = 3x² + 30x

⇒ 3x² - 135x - 750 = 0

⇒ x² - 45x - 250 = 0

⇒ x² - 50x + 5x - 250 = 0

⇒ x(x - 50) + 5(x - 50) = 0

⇒ (x - 50) (x + 5) = 0

⇒ x - 50 = 0 or x + 5 = 0

⇒ x = 50, - 5 (As x can't be negative)

⇒ x = 50 km/h

Hence, the original speed of the bus was 50 km/h.

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