You are on the south side of a river and you need to cross the river in order to get to a campsite. Notonly is the campsite on the north side of the 0.25 mile wide river, it is also 1 mile east upstream. Youwalk at a pace of 3 miles per hour, but the current of the river forces you to swim at a rate of 2 milesper hour. How far east should you walk before swimming directly to the campsite?
Accepted Solution
A:
Answer:Width of river = 0.25 mileAs length of river is not given , but it is given that campsite is located 1 mile east upstream, So length of river = 1 mileSpeed of mine in river while going upstream = 3 miles per hourSpeed of current as going Upstream = 1 miles per hourNow Reduced speed of mine = Speed of mine in river while going upstream - Speed of current as going Upstream = 3 - 1 = 2 miles per hour1. There are two ways to reach campsite (a) either walk 1 mile from starting point in east direction and then swim 0.25 mile in North direction to reach campsite.Or(b) From the starting point Considering a right triangle having, base=1 mile and altitude = 0.25 mile, then finding the length of hypotenuse using formula = [tex]\sqrt{(altitude)^2 + (Base)^2[/tex] =[tex]\sqrt{.25^2+1^2}[/tex]=√1.0625=1.03078(approx)⇒ you must walk a distance of 1 mile in the east direction and then swim 0.25 mile north direction to reach directly at campsite.[shown in the diagram]