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.
1. Draw a labeled diagram of the scenario.
2. Daniel can swim at an average rate of 150 feet per minute. How many minutes does it take him to swim to the boat ramp? Round your answer to the nearest hundredth.
3. How far is the boat ramp from the campsite? Round your answer to the nearest hundredth.
4. Daniel can jog at 4 miles per hour. How many minutes does it take him to jog from the boat ramp to the campsite? Round your answer to the nearest hundredth.
5. 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.