Question

. A train travels some distance with a uniform speed.

If the speed of the train is reduced by 24 km/hr.

then it takes 6 hours more. If its speed is again

reduced by 9 km/hr. due to bad weather then it

takes

48/
5

hours more than the scheduled time. Then

find the original travel time​

Answer 1

Answer:

The original travel time is 16 hours

Step-by-step explanation:

Let the distance be d, speed of the the train v and the original time t

Distance = speed × time

∴ d = v × t

if speed is reduced by 24 km/h, the time taken is 6 hour more

Thus,

d = (v - 24) × (t + 6)

or, vt - 24t + 6v - 144 = vt

or, -4t + v = 24    .......... (1)

Again if its speed is further reduced by 9 km.h, it takes 48/5 hours more

Thus,

d = (v - 33) × (t + 48/5)

or, vt - 33t + 48v/5 - 1584/5 = vt

or, -165t + 48v = 1584

or, -55t + 16v = 528    .......... (2)

Multiplying eq (1) by 16 an subtracting it from eq (2)

-55t + 64t = 528 - 384

9t = 144

t = 16 hours

Thus, the original travel time is 16 hours.