Question

A train travels at a certain average speed for a distance of 63 km

Answer 1

Step-by-step explanation:

Let original speed of the train be x km/h.

Time taken to travel 63 km = 63/x hours

New speed = (x + 6) km/hr

Time taken to travel 72 km = 72/(x + 6) hours

According to the question,

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

x2 - 39x - 126 = 0

(x - 42)(x + 3) = 0

x = -3 or x = 42

As the speed cannot be negative, x = 42

Thus, the average speed of the train is 42 km/hr.

Answer 2

Let original speed of the train be x km/h.

Then, time taken to travel 63 km = 63/x hours

New speed = (x + 6) km/hr

Time taken to travel 72 km = 72/(x + 6) hours

According to the question,

63/x + 72/x+6=3

after taking LCM

(63x+378+72x/)x^2+6x=3

135x+ 378= 3x^2+18x

3x^2-117x-378=0

x2 - 39x - 126 = 0

(x - 42)(x + 3) = 0

x = -3 or x = 42

As the speed cannot be negative, x = 42

Thus, the average speed of the train is 42 km/hr.