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 54km`=54/x h`        `(Time=(Distance)/(Speed))` 

New speed of the train =`(x+6)`km/h  

∴ Time taken to cover 63km=`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(x^2+6x)` 

⇒`3x^2-99x-324=0` 

⇒`x^2-33x-324=0` 

⇒`x^2-33x-108=0` 

⇒`x^2-36x+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.