Rima and Maisha start walking from P to Q at 7 and 3 kmph respectively. Rima reaches Q and starts back for P. How far from Q will she meet Maisha if the distance between P and Q is 24 km?

Question: Rima and Maisha start walking from P to Q at 7 and 3 kmph respectively. Rima reaches Q and starts back for P. How far from Q will she meet Maisha if the distance between P and Q is 24 km?

Solution:
Let Rima and Maisha will meet at a distance of x km from point Q
Rima travels = (24 + x) km and Maisha travels = (24 - x) km
Since, their traveling time is the same.
Then,
(24 + x)/7 = (24 - x)/3
⇒ (24 - x) × 7 = (24 + x) × 3
⇒ 168 - 7x = 72 + 3x
⇒ 10x = 96
∴ x = 9.6
∴ Rima and Maisha will meet at a distance of 9.6 km from point Q.