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# Math help / trig?

Daniel stands on one side of a stream that is 400 feet wide. He wants to reach his campsite on the opposite side of the stream. The campsite is 1600 feet away from the point directly opposite where Daniel stands. He decides that he will swim to the boat ramp to get to the side of the stream the campsite is on, and then jog to the campsite. The angle formed by Daniel’s swim path and the shore at the boat ramp is 53 degrees

1. Daniel arrives at his campsite out of breath from his swim and jog. His sister tells him that he should have swam to the boat ramp that is only 200 feet from the campsite and then jogged. She claims that he would have arrived quicker this way.

Is Daniel’s sister correct? Support your answer mathematically.

### 2 Answers

- ToddLv 71 month agoFavorite Answer
Not enough info to form the geometry. I'm guessing the second route is shorter if the swim and jog rate are the same. Here's how I picture with the swim longer, approach angle much more acute. One can easily show that the first route (uppermost one) is the longer one. Just find the hypotenuse for each swim. To the first (400 / cos(37)) you add the other hypotenuse, to the second hyp (sqrt of 1600^2 + 400^2 you add 200'. Actually you could move the second ramp closer to Daniel's starting position. I just did it this way to make it simpler to draw. If you move the small circle closer, the hypotenuse is then sqrt of (1400^2 + 400^2).+ 200.

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- PuzzlingLv 71 month ago
You're missing information about his rate of swimming and his rate of jogging. I suggest writing down what you figured out for the first part of this question (about the time it took going at 53°).

You basically need the distance traveled diagonally in the river to the first boat ramp and how far he jogs along the shore to the campsite. Use the two (missing) rates to find his time.

Then do the same thing, but this time he is swimming the diagonal to the second boat ramp (200 ft from the campsite) and then the last 200 feet jogging to the campsite.

Is it faster going Daniel's way or the sister's way?

I suggest drawing a diagram and it should help considerably. Post your diagram.

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