A passenger train takes one hour less for a journey of 150 km if its s

1.	A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from the usual speed. Find the usual speed of the train.
Answer» Time = distance/speed Let the speed of the train be ‘a’ km/hr. Given, passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from the usual speed. \(\Rightarrow \frac{150}{a}-\frac{150}{a+5}=1\) ⇒ 150(a + 5 – a) = a² + 5a ⇒ a² + 5a – 750 = 0 ⇒ a² + 30a – 25a – 750 = 0 ⇒ a(a + 30) – 25(a + 30) = 0 ⇒ (a – 25)(a + 30) = 0 ⇒ a = 25 km/hr

A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from the usual speed. Find the usual speed of the train.

Answer»

Time = distance/speed

Let the speed of the train be ‘a’ km/hr.

Given, passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from the usual speed.

\(\Rightarrow \frac{150}{a}-\frac{150}{a+5}=1\)

⇒ 150(a + 5 – a) = a² + 5a

⇒ a² + 5a – 750 = 0

⇒ a² + 30a – 25a – 750 = 0

⇒ a(a + 30) – 25(a + 30) = 0

⇒ (a – 25)(a + 30) = 0

⇒ a = 25 km/hr