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?

Answer 1

Answer:

Vb tb = L = Va ta = 50      (I)

Va * 1 + Vb * 1 = 50  = Va + Vb  when they cross

ta = tb - 5/6     (II)

(50 - Va) * (ta + 5/6) = Va ta   using (I) and (II)

50 ta + 250/6 - Va ta - 5/6 Va = Va ta

300 ta + 250 - 5 Va = 0       since Va ta = 50

300 Va ta + 250 Va - 5 Va^2 = 0     multiply by Va

Va^2 + 70 Va - 3000 = 0

Va = 30

then Vb = 20

ta = 5/3 and tb = 5/2

5/3 + 5/6 = 5/2 = tb