Question

Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels $5km/hr$ faster than the second train. If after two hours, they are $50km$ apart, find the average speed of each train.

Answer 1

Let the average spped of the second train be $xkm/h$.

Thus, the speed of the first train will be $(x+5)km/h$.

Distance travelled by the first train in two hours $=2(x+5)km/h$

Distance travelled by the second train in two hours $=2xkm/h$

Using pythagoras theorem, we have

$4x^2+4(x+5{)}^2={50}^2$

$4x^2+4x^2+40x+100=2500$

$8x^2+40x-2400=0$

$x^2+5x-300=0$

$(x-15)(x+20)=0$

$x=15,-20$

Ignore the negative value of the speed. We have,

Speed of the second train be $15km/h$.

Spped of the first train be $(15+5)=20km/h$.