There are 2 points A and B in a river which is flowing at 5kmph. Distance between A and B is 300 kms. Two boats with speed 10 kmph and 15 kmph (in still water) start at A and B respectively. When will the boats meet first time and second time?

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There are 2 points A and B in a river which is flowing at 5kmph. Distance between A and B is 300 kms. Two boats with speed 10 kmph and 15 kmph (in still water) start at A and B respectively. When will the boats meet first time and second time?

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To answer the question, first I have to **assume** the following:

a: river flows from A to B

b: boat-1 starts from point A toward point B and boat-2 starts from point B toward point A

c: second meeting occurs after boat-1 arrive at point B and boat-2 arrive at point A and then both boats return to point of origin

**First meeting:** 12 hours

boat-1 and boat-2 meet at point C which is L1 km from A or (300-L1) km from B in T1 hours

boat-1 relative speed = (10+5) = 15 kph and boat-2 relative speed = (15-5) = 10 kph

boat-1 travels 15 x T1 = L1 and boat-2 travels 10 x T1 = 300 - L1 -----> L1 = 180 km

First meeting is 180 km : 15 kph = 12 hours

**Second Meeting:** 40 hours

boat-1 arrives at B in (300 km : 15 kph) = 20 hours and boat-2 arrives at A in (300 km : 10 kph) = 30 hours

when boat-2 returns to origin, boat-1 has traveled to origin (30 - 20) = 10 hours

boat-1 returns with relative speed (10 - 5)= 5 kph and boat-2 (15 + 5)= 20kph

boat-1 and boat-2 meet at point D which is L2 km from A in T2 hours or (300-L2) km from B in (T2+10) hours

boat-2 relative speed = (15+5) = 20 kph and boat-1 relative speed = (10-5) = 5 kph

boat-2 travels 20 x T2 = L2 and boat- travels 5 x (T2+10) = 300 - L2 -----> L2 = 200 km

Second meeting is (200 km : 20 kph) + 30 hours = 40 hours since time of start

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