find the speed of each train.

Question

if the 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 hrs, they are 50 km apart.

Answer 1

Lets call the first train distance TA and the second trains distance TB.

The distance between the 2 will be sqrt (TA² + TB² )

distance = rate * time.

 

So, TA = (r+5) * time = (r+5) * 2 = 2r + 10, TB = r * time = 2r

since the distance is 50, and distance = sqrt (TA² + TB² )

 

50 = sqrt (TA² + TB² )

50 = sqrt((2r+10)² + (2r)²

50 = sqrt(4r² + 40r + 100 + 4r² )

50 = sqrt(8r² + 40r + 100)

(square both sides)

2500 = 8r² + 40r + 100

8r² + 40r - 2400 = 0

8*(r + 20)(r-15) = 0

r = -20 and 15

speed is not negative, so train 1 is 20 km/hr and train 2 is 15km/hr