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 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.

Answer 1

Let the speed of the train moving in west direction be $x\frac{km}{hr}$

∴ Speed of the train moving in the North direction = \( (x + 5) \frac{km}{hr}\)

Distance covered by the train moving in West direction in 2 hours,

$OB=x\frac{km}{hr}\times 2hr=2xkm$
[ ∵ Distance = Speed × Time]

Distance covered by the train moving in North direction in 2 hours,

$OA=(x+5)\frac{km}{hr}\times 2hr=(2x+10)km$

Distance between the two trains after 2 hours, AB = 50 km
(Given)

In ∆OAB,

$O{A}^2+O{B}^2=A{B}^2$

$(2x+10{)}^2+(2x{)}^2=(50{)}^2$

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

$8x^2+40x–2400=0$

$x^2+20x–15x–300=0$

$x(x+20)–15(x–20)=0$

$(x+20)(x–15)=0$

$x+20=0$ or $x–15=0$

Either x = –20

or x = 15

$\therefore x=15(\because Speedofthetraincannotbenegative$

Putting the value of x=15 in x + 5 we have 15 + 5 = 20.

Thus, the speed of the two trains is $15\frac{km}{hr}and20\frac{km}{hr}$