From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hours. If A traveled with 2/3 of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is:

Question: From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hours. If A traveled with 2/3 of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is:

Solution:
Let the speed of A = x km/h and that of B = y km/h

According to the question;
(x × 6) + (y × 6) = 60
Or, 6x + 6y = 60
Or, 6(x + y) = 60
Or, x + y = 10 --------- (i)

And,
(2x/3) × 5 + (2y × 5) = 60
Or, (10x/3) + 10y = 60
Or, (10x + 30y)/3 = 60
Or, 10x + 30y = 180
Or, 10(x + 3y) 180
∴ x + 3y = 18 ---------- (ii)

From equation (i) × 3 - (ii)
3x + 3y = 30
x + 3y = 18
Or, 2x = 12
∴ x = 6 km/h