Question

Two trains leaves 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 second train. If after two hours, they are 50km apart,find the speed of each train. ​

Answer 1

2 hour=time

x=speed of 2nd train

x+5=speed of 1st train

so, distance of 1st= 2*(x+5)km = 2x +10

dist 2nd= 2x km

(by pythagorous)

sq(50)=sq(2x) + sq(2x+10)

2500= 8x^2 + 40x+ 100

x^2 + 5x-300=0

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

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

SO,

x=15

x= -20 (immposible)

hence,

speed of 1st train=40 km/h

speed of 2nd train =15 km/h

Answer 2

⚡⚡ÀÑSWËR⚡⚡

$time = 2hours \\ \: speed \: of \: 2nd \: train \: = x \\ speed \: of \: 1st \: train = (x + 5) \\ so \: \\ distance \: of \: 1st \: train \: = 2(x + 5)km \\ \\ = 2x + 10 \\ \\ distnce \: covered \: by \: 2nd \: train \\ = 2km \\ \\ \\ \\ by \: pythagoras \: theorem \\ {50}^{2} = {2x}^{2} + {(2x + 10)}^{2} \\ 2500 = {18x}^{2} + 40x + 100 \\ x(x + 20) - 15(x + 20) = 0 \\ (x - 15)(x + 20) = 0 \\ \\ \\ \\ x = 15 \\ x = - 20 \\ (which \: is \: not \: possible) \\ \\ so \\ \\ speed \: of \: 1st \: train \\ \: = 40km \: per \: hour \\ \\ \\ \\ speed \: of \: 2nd \: train \\ = 15km \: per \: hour$