Question

A fast train takes 3 hours less than a slow train for a journey of 600 kms. If the speed of the slow train is 10 km/hr less than the fast train, find the speed of the fast train.

A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/h less than that of the fast train, find the speed of each train.

Answer 1

Let the speed of the slow train be S, Hence speed of the fast train = S + 10. 

D = 600 km, Time = Distance/Speed, Time difference = 3 hours 

Hence, in these two conditions,

`600/"s" - 600/("s"  + 10) = 3`

⇒ 600 × (s + 10) – 600 × S = S × (S + 10) × 3 

⇒ 3s² + 305 – 6000 = 0 

⇒ S² + 10S – 2000 = 0 

⇒ S² + 50S – 40s – 2000 = 0 

⇒ S (S + 50) – 40 (S + 50) = 0 

⇒ (S + 50) (S – 40) = 0 

As the speed can’t be negative, S = 40 km/ hr 

Hence, speed of the fast train = 40 + 10 = 50 km/hr. 

Answer 2

Total distance of a journey = 600 km

Let speed of fast train be x km/hr, then speed of slow train = (x – 10) km/hr

According to the questions,

`600/(x - 10) - 600/x = 3`   ...`[∵ "Time" "Distance"/"Speed"]`

⇒ `600 [(x - x + 10)/((x - 10)x)] = 3`

⇒ `6000/(x^2 - 10x) = 3`

⇒ x² – 10x – 2000 = 0

⇒ x² – 50x + 40x – 2000 = 0

⇒ x(x – 50) + 40(x – 50) = 0

⇒ (x – 50) (x + 40) = 0

Either x = 50 or x = – 40   ...[∵ Speed can not be possible is negative]

So, the speed of fast train = 50 km/hr and the speed of slow train = 50 – 10 = 40 km.