A and B start at the same time from two places 30 km apart. If they walk in the same direction, A overtakes B in 10 hours and if they walk in opposite directions they meet in 2 hours. Find the rate of walking of A.
9 kmph
Let the two places P1 and P2 be 30 km apart and let A start from P1 and B from P2.
Let A’s speed of walking be x km/hr and B’s speed by y km/hr. According to the question, when they walk in the same direction .
10 (x – y) = 30 …(i)
When they walk in opposite direction
2(x + y) = 30 …(ii)
On dividing (i) by (ii), we get
5(x−y)x+y=1⇒5x−5y=x+y⇒4x−6y=0...........(iii)
On multiplying (ii) by 2, we get
4x+4y=60 ........................(iv)
⇒ - 6y - 4y = - 60
⇒ -10y = - 60
⇒ y = 6
On substituting value of y in (iv)
⇒ 4x + 4×6 = 60
⇒ 4x+24=60
⇒ 4x=36
⇒ x=364=9
∴ A’s speed = 9 km/hr and B’s speed = 6 km/hr.