Question

14. Two boatmen start simultaneously from
the opposite shores of a river and they
cross each other after 45 minutes of
their starting from the respective shores.
They rowed till they reached the
opposite shore and returned
immediately after reaching the shores.​

Answer 1

Answer:

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.