Question

a train covered a certain distance at uniform rate on increasing its speed by 5 km per hour it saves 20 minutes and on increasing its speed by 20 km per hour it loses 2 hours find the distance covered by the train

Answer 1

Let the speed of train be u. Let the train travels S km in time t

So ,

We know that

$speed = \frac{distance}{time} \\ \\ u = \frac{s}{t} \\ \\ s = ut$

According to first condition;

if it's speed increase by 5 km per hour it saves 20 minutes or 1/3 hour

$s = (u+5)(t-1/3) \\ \\ 3ut = (u+5)(3t-1) \\ \\ 3ut = 3ut - u + 15t - 5 \\ \\ u - 15t = -5 \\ \\ 15t - u = 5$

Again if increasing its speed by 20 km per hour it loses 2 hours

$s = (u - 20)(t+2) \\ \\ ut = ut + 2u - 20t - 40 \\ \\ 2u - 20t = 40 \\ \\ u - 10t = 20$

Adding equations we get ,

25t = 25

t = 1 hour

putting t = 1 in first equation ,

u -10 = 20

u = 30km/hour

Hence,

S = ut = 30km

S = 30 km