Question

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6km/hr more than its original speed if it take 2 hr to complete total journey what is the original average speed ?

Answer 1

A train travels at a certain average for a distance of 63km and then travels a distance of 72km at an average speed of 6km/hr more than its original speed.

If it takes 3 hours to complete the total journey,what is its original average speed.

Original-speed DATA:
distance = 63 km ; rate = x km/hr ; time = 63/x hrs.

Faster-speed DATA:
distance = 72 km ; rate = (x+6)km/hr ; time = 72/(x+6) hrs.

Equation:
time + time = 3 hrs

63/x + 72/(x+6) = 3 hrs

63(x+6) + 72x = 3x(x+6)
21(x+6) + 24x = x(x+6)
45x + 21*6 = x2+6x
x2-39x-21*6 = 0
x2-39x-126 = 0
(x-42)(x+3) = 0

Positive solution:
x = 42 km/hr (original rate)

Answer 2

Solutions :-

We know,
Distance = Speed × time
Speed = distance/time
Time = distance/speed

We have,
Distance travels on certain speed = 63 km
Let Original speed of train be x
Distance travels at speed of 6 km/hr = 72 km
Speed = (x + 6) km per hour
Time = 72/(x+6) hrs
Total journey completed in 3 hrs

Find the value of x :-

A/q

=> 63/x + 72/(x + 6) = 3
=> 63(x + 6) + 72x = 3x(x+ 6)
=> 21(x + 6) + 24x = x(x+6)
=> 45x + 21×6 = x2 + 6x
=> x^2 -  39x - 126 = 0
=> x^2 - 39x - 126 = 0
=> x^2-42x+3x -126=0
=> x(x-42)+3(x-42)=0
=> (x - 42)(x + 3) = 0
=> x = 42 or x = -3


Answer : Original average speed = 42 km per hr


Note :- Distance is always in positive