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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°

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

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.

Feb 5, 2020
edited by Bmathhelp  Feb 5, 2020
edited by Bmathhelp  Feb 5, 2020
edited by Bmathhelp  Feb 5, 2020
edited by Bmathhelp  Feb 5, 2020

#1
+2

Feb 5, 2020
#2
+2

1.  We have something like this

D

1200

B  ___________ C

53°

400           -

-

A

A  = point where he stands

B =  point on opposite shore directly across  from Daniel

C =  boat ramp

D =  his campsite

2.  We  can find the distance he swims  (A to C)  as follows

Triangle  ABC  is a right triangle  with angle  ABC  = 90°

And AC  is the hypotenuse

And  AB  is the opposite side to the 53° angle

So

sin 53°  =   400 / AC         rearrange as

AC  =  400 / sin 53  ≈   500.85 ft

So....the time it takes to swim this distance  is

500.85   / 150   ≈    3.34  min

3.  To answer this....we need to  first know the distance BC.....this is given by

tan 53°  =  400 / BC      rearrange as

BC  =  400 / tan 53°  ≈    301.42 ft

And  DBC  is a right triangle with  hypotenuse  DC.....this is the distance from the boat ramp to the campsite

So

DC  = sqrt (DB^2 + BC^2)

DC =  sqrt ( 1200^2 + 301.42^2 )  ≈  1237.28  ft

4.  Time it takes to jog to the campsite from the boat ramp  =

Note :  4mph   =  4 * 5280  / 3600  =   88/15  ft / sec

So     distance / rate  = time   ....so....

1237.28  /  (88/15)   =

1237.28 * 15  /  88  =  210.9  sec  ≈    210.9/60  ≈  3.52  min   Feb 5, 2020
#3
+2

And I see EP found an even earlier answer of mine.

Half the infor was missing then.  On scanning this new question, some of the required info is still missing.

You did not even bother to comment on my comprehensive answer!

I guess you are just another brat here who reposts without comment when they do not get the answer that they want.