Question

A train takes 2 hours less for a journey of 300 km if it's speed is increased by 5 km/hour from it's usual speed. Find the usual speed of the train.

Answer 1

Answer:

Total distance =300km

Let usual speed be x km/hr

And time taken be t hrs

=>300/x=t -equation 1

If speed is increased by 5km/hr

Speed=x+5

And time decreased by 2 hrs

Then time =t-2

=>300/x+5=t-2

From eq 1

300/x+5=300/x-2

=>300/x+5=300-2x/x

300x=(300-2x)(x+5)

300x=300x+1500-2x^2-10x

0=-2x^2-10x+1500

2x^2+10x-1500=0

X^2+5x-750=0

x^2+30x-25x-750=0

x(x+30)-25(x+30)=0

(x-25)(x+30)=0

x=25 & x=-30(rejected as speed cannot be negative)

hence speed =25km/hr