Question

You are on the south side of a river and you need to cross the river in order to get to a campsite. Not
only is the campsite on the north side of the 0.25 mile wide river, it is also 1 mile east upstream. You
walk at a pace of 3 miles per hour, but the current of the river forces you to swim at a rate of 2 miles
per hour. How far east should you walk before swimming directly to the campsite?

Answer 1

Answer:

Width of river = 0.25 mile

As length of river is not given , but it is given that  campsite is located 1 mile east upstream, So length of river = 1 mile

Speed of mine in river while going upstream = 3 miles per hour

Speed of current as going Upstream = 1 miles per hour

Now Reduced speed of mine = Speed of mine in river while going upstream - Speed of current as going Upstream

                                              = 3 - 1

                                              = 2 miles per hour

1. 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 = $\sqrt{(altitude)^2 + (Base)^2$

=$\sqrt{.25^2+1^2}$

=√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]