CAT4MBA

Question: You are paddling your canoe upstream at a constant velocity. After paddling for six miles, the wind blows your hat into the stream and the hat begins flowing downstream. You continue to paddle upstream for two more hours before noticing that your hat is missing, at which time you turn around and paddle downstream at the same rate you had paddled upstream, overtaking your hat just as you return to your original starting point.

What is the speed of the boat?

What is the speed of the current?

 What is the distance between the start point and the point at which you crosses the hat?

Solution:

Let us suppose that the speed of the boat in still water is 'x' miles per hour and that os the current is 'y' miles per hour.

Now, the upstream speed = (x - y) miles per hour and

the downstream apeed = (x + y) miles per hour

So, the time taken by the boat to cover 6 miles upstream is: 6/(x - y) hours.

Then it travels for 2 more hours upstream thus covering a distance of 2(x - y) miles.

In that same two hours, the hat was being carried along with the current and thus the hat had covered a distance of 2y miles.

So, the distance between the boat and the hat now is: 2(x - y) + 2y = 2x miles.

So, the distance of the boat from the starting point is: {2(x - y) + 6} miles and that of the hat from the starting point is: (6 - 2y) miles.

Now, the time taken by the hat to cover this (6 - 2y) miles is the same as the time taken by the boat to cover {2(x - y) + 6} miles.

That is:

(6 - 2y)/y = {2(x - y) + 6}/(x + y)

or, (6 - 2y)(x + y) = {2(x - y) + 6}(y)

or, 6x - 2xy + 6y - 2y² = 2xy - 2y² + 6y

or, 6x = 4xy

or, y = 6/4 = 1.5

Hence, the speed of the stream is 1.5 miles per hour.

Thank You.

Ravi Raja

Does that mean other two answers are cant be determined/ None of the above