Question

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

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

Original speed be p km/h

Also

Time taken = 75/p hrs

New speed = p + 10 km/h

Time taken to cover 90 km with new speed

= 90/p + 10

Situation,

75/p + 90/(p + 10) = 3

75(p + 10) + 90p/p(p + 10) = 3

165p + 750 = 3p² + 30p

3p² - 135p - 750 = 0

p² - 45p - 250 = 0

p² - 50p + 5p - 250 = 0

p(p - 50) + 5(p - 50) = 0

(p - 50) (p + 5) = 0

p - 50 = 0 or p + 5 = 0

p = 50, - 5 (Negative value is not applicable)

⇒ p = 50 km/h

Therefore,

Speed of the bus was 50 km/h.