Question

Two boats on the opposite shores of a river start moving towards each other. When they pass each other they are 750 yards from one shoreline. They each continue to the opposite shore, immediately turn around and start back. When they meet again they are 250 yards from the other shoreline. Each boat maintains a constant speed throughout . How wide is the river ( in yards)?

Answer 1

Let width of the river is D and distance covered by boat A and B are a and b respectively.
Sum of distance covered by A and B will be width of the river for the first meet.
D = a + b..............(1)
Given, when they pass each other they are 750 yards from one shoreline , it means one of the boat has covered 750 yards . Say that boat is A.
a = 750 yards.............(2)
By the second passing, each boat has covered the width of the river, and turned around. Then, together the boats have covered width of the river once more, so the sum of the distances they have traveled is three times with width of the river. Since they travel at a constant rate, and together they have gone three times as far as when they first passed, it follows that one of them has traveled a distance of 3a and the other has traveled 3b.
When the boats passes a second time, 250 yards from the "other" shoreline , it follows that the same boat has traveled 750 yards by their first passing has traveled D + 250 yards by the second passing.
3a = D + 250...........(3)
Now, putting value of eq. 2 in eq . 1
3 *750 = D+ 250
D = 2000 yards.