Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?

Question: Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?

Solution:
If the speed of the faster horse be f and that of slower horse be s
Then,
f + s = 50/1 = 50 km/h
∴ f = 50 - s

ATQ,
50/s - 50/f = 5/6
⇒ (50f - 50s)/(sf) = 5/6
⇒ 50(f - s) = (5/6)(sf)
⇒ 50(50 - s - s) = (5/6)(sf)
⇒ 6(2500 - 100s) = 5 × s × (50 - s)
⇒ 15000 - 600s = 250s - 5s²
⇒ 5s² - 600s - 250s + 15000 = 0
⇒ 5s² - 850s + 15000 = 0
⇒ s² - 170s + 3000 = 0
⇒ s² - 150s - 20s + 3000 = 0
⇒ s(s - 150) - 20(s - 150) = 0
⇒ (s - 150)(s - 20) = 0
∴ s = 150, 20 [ 150 not be acceptablr]

∴ The speed of the slower horse is 20 km/h