sarah asked in Science & MathematicsMathematics · 1 month ago

# trig question ?

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 .- Draw a labeled diagram of the scenario-

1. 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.

2. How far is the boat ramp from the campsite? Round your answer to the nearest

Relevance
• 1 month ago

(I agree with C.M, that there should be a diagram; however, I will make an assumption that Daniel swims directly towards the opposite shore -- and thus gets swept downstream as he swims, reaching the boat ramp immediately he reaches the shore.   However, we also need the speed of the current.  I wil make an even more rash assumption: the river flows at 50 ft/minute -- not unreasonable speed; and one can adjust the calculations to account for any speed.)

The river is 400 ft wide; and he swims at 150 ft/minute.

400 / 150 = 8/3 = 2 2/3 = 2.67 (nearest hundredth).

Hence, he takes 2.67 minutes to reach the boat ramp.

2.67 * 50 = 133.5  (properly 133 1/3)

That is, he has been swept 133.5 ft downstream.

1600 - 133.5 = 1466.5 ;

and the distance to camp from the boat ramp is 1466.5 ft.