Question

A train travels at a certain average speed for a distanced of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Answer 1

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

Time taken to cover 54 km = `54/x h`   ...`("Time" = "Distance"/"Speed")` 

New speed of the train = `(x + 6) (km)/h`  

∴ Time taken to cover 63 km = `63/(x+6) h` 

According to the given condition,

Time taken to cover 54 km + Time taken to cover 63 km = 3 h 

∴ `54/x + 63/(x + 6) = 3` 

⇒ `(54x + 324 + 63x)/(x(x + 6)) = 3` 

⇒ 117x + 324 = 3(x² + 6x)

⇒ 117x + 324 = 3x² + 18x 

⇒ 3x² – 99x – 324 = 0 

⇒ x² – 33x – 324 = 0 

⇒ x² – 33x – 108 = 0 

⇒ x² – 36x + 3x – 108 = 0 

⇒ x(x – 36) + 3(x – 36) = 0 

⇒ (x – 36)(x + 3) = 0 

⇒ x – 36 = 0 or x + 3 = 0

⇒ x = 36 or x = –3 

∴ x = 36   ...(Speed cannot be negative)

Hence, the first speed of the train is 36 km/h.