# You are at a point A in a field separated from a friend at point B on the other side of a river…. 1 answer below »

You are at a point A in a field separated from a friend at point B on the other side of a river. Your friend is in need and you have to reach him or her as soon as possible. The river is 20 m wide and flows in a direction perpendicular to the direct line of sight between you at point A and your friend at point B. The nearest point on the river bank closest to you is 80 metres away. Your friend is 50 metres away from the nearest point on the opposite side of the river. You are able to run 7 metres per second on land and swim 1 metre per second across the river, perpendicular to the flow. You run directly to a point P that you have chosen on the left bank of the river, located z metres perpendicular to, and to the left, of your line of sight with your friend, and enter the river at P. It takes 20 seconds for you to swim across the river. From the point Q, where you exit the river on the right bank, you run directly to reach your friend. Suppose the river is flowing uniformly downstream (to your right as you look from A to B towards your friend) and carries you F metres per second downstream for the time you are in the river. Let D be the distance you are carried downstream as you swim across the river, as in the diagram on the next page.

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