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Peter belongs to Town A and Paul belongs to Town B. They start their journeys towards each other’s towns following the same route at the same time. They meet somewhere on the way and continue with their journeys. After meeting Paul, Peter takes another 13.5 hours to reach his destination while Paul takes another 6 hours to reach Peter’s town. If Peter travelled at the speed of 30 km/h, what was Paul’s speed in km/h?

Peter belongs to Town A and Paul belongs to Town B. They start their journeys towards each other’s towns following the same route at the same time. They meet somewhere on the way and continue with their journeys. After meeting Paul, Peter takes another 13.5 hours to reach his destination while Paul takes another 6 hours to reach Peter’s town. If Peter travelled at the speed of 30 km/h, what was Paul’s speed in km/h? Correct Answer 45

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At x hours later and Paul meet each other.

Distance (d) = (Relative speed) × time

Given that the speed of Peter = 30 km/hr

Let speed of Paul = y km/hr

Let the distance between Town A and Town B be d

⇒ d = (30 + y) × x         ----(1)

Given that Paul takes another 6 hours after meeting peter to reach town B.

⇒ d = y(x + 6)         ----(2)

Similarly, Peter takes another 13.5 hours after.

Meeting Paul to reach town A.

⇒ d = 30(x + 13.5)         ----(3)

From equation (1) & (2)

⇒ (30 + y)x = y(x + 6)

⇒ 30x + xy = xy + 6y

⇒ 30x = 6y

⇒ y = 5x

From equations (1) & (3)

⇒ (30 + y)x = 30(x + 13.5)

⇒ 30x + xy = 30x + 30 × 13.5

⇒ xy = 30 × 27/2

⇒ xy = 15 × 27

⇒ x2 = 81

⇒ x = 9

⇒ y = 5 × 9 = 45 km/hr

∴ Speed of Paul = 45 km/hr

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