Question

Daniel stands on one side of a stream that is 400 feet wide. He wants to reach his campsite that is 1600 feet downstream on the opposite side. He decides he will swim to the boat ramp on the opposite side, which is part way downstream toward the campsite, then jog the rest of the way. The angle formed by Daniel’s swim path and the shore at the boat ramp is 53 degrees.
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.
answer: 3.34 minutes
3. How far is the boat ramp from the campsite? Round your answer to the nearest
answer: 1,237.28 feet
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.
answer: 3.52 minutes
5. Daniel arrives at his campsite out of breath from his swim and jog. His sister tells him that he should have swum 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.

Answer 1

The time that will be taken for Daniel to swim to the boat ramp will be 3.34 minutes.

How to calculate time taken

Let the distance be x.

Based on the information given, the calculation will be:

Sin 53° = 400/x

0.7986 = 400/x

x = 500 feet

Time = Distance / Speed

Time = 500/150 = 3.33 minutes.

The distance of the boat ramp from the campsite will be:

Cos53° = y/500

0.60 = y/500

y = 300 feet.

Distance will be:

= 1600 - 300 = 1300 feet

The minutes that it takes him to jog from the boat ramp to the campsite will be:

Distance = 1300 feet

Rate = 4 miles per hour = 352 feet per minutes

Time = Distance / Rate

Time = 1300/352 = 3.69 minutes

The total time taken will be:

= 3.33 + 3.69

= 7.02 minutes

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