Question

If the average speed of a train is increased
by 10 km/hr , the time taken to travel a
certain distance is reduced by 36 minutes. If
the average speed is reduced by
15 km/hr, the train takes 1hr and 12 mins
more to travel the same distance. Calculate
the average speed of the train.
Solution:
ca cneed of the train be x km/hr.​

Answer 1

Answer:

The average speed of train is 90 km/h  .

Step-by-step explanation:

Given as :

The distance cover by train = d km

Let The average speed of train = s km/h

Let The time taken to cover d distance = t h

According to question

The average speed of a train is increased by 10 km/hr , the time taken to travel a  certain distance is reduced by 36 minutes.

∵ Distance = speed × time

i.e d = s t

Or, d = (s + 10) km/h × (t - $\dfrac{36}{60}$) h

Or, st = (s + 10) × (t - 0.6)                  

Or st = st - 0.6 s + 10 t - 6          

Or, 0.6 s - 10 t + 6 = 0                ..........1

Again

If  the average speed is reduced by  15 km/hr, the train takes 1 hr and 12 mins  more to travel the same distance.

So, Time = 1 h + 12 m = 1.2 h             [∵ 60 min = 1 h]

∵ Distance = speed × time

Or, d = (s - 15) km/h × (t h + 72 m)

Or, st = (s - 15) km/h × (t + 1.2) h  

Or, st = st + 1.2 s - 15 t - 18

Or, 1.2 s - 15 t - 18 = 0                     ..........2

Form eq 1 and eq 2

(1.2 s - 15 t) - 2 × (0.6 s - 10 t) = 18 + 2 ×6

Or, (1.2 s - 1.2 s) + (20 t - 15 t) = 30

Or, 0 + 5 t = 30

∴   t = $\dfrac{30}{5}$

i.e  t = 6 hours

So, Time taken by train = t = 6 hours

Put the value of t in eq 2

∵ 1.2 s - 15 t = 18

Or, 1.2 s - 15 × 6 = 18

or, 1.2 s = 18 + 90

Or, 1.2 s = 108

∴  s = $\dfrac{108}{1.2}$

i.e s = 90 km/h

So, The average speed of train = s = 90 km/h

Hence, The average speed of train is 90 km/h  . Answer