Question

Jim goes canoeing on a local stream that has been measured to flow at 2 mph. If he can go 9 miles upstream in the same time it takes him to go 15 miles downstream, find how fast he can go in still waters.

Answer 1

Time taken to go downstream = 4 / ( 2 + S) where S is the speed of the river

TIme taken to go upstream = 1 / ( 2 - S )

Since the time taken is the same in each case we can equate both of them

1 / ( 2 - S) = 4 / ( 2 + S )

2 + S = 8 - 4S

5 S = 6

S = 6 / 5

= 1.2 mph

Answer 2

Answer: This is a problem of solving a system of linear equations. Let x be the speed of Jim in still waters, and y be the speed of the stream. Then we have:

{x+y=15/tx−y=9/t​

where t is the time it takes Jim to go upstream or downstream. We can solve this system by adding the two equations and eliminating y:

2x=24/tx=12/t

Then we can substitute x into one of the equations and solve for y:

y=15/t−12/ty=3/t

Since we know that the speed of the stream is 2 mph, we can equate y to 2 and solve for t:

3/t=2t=3/2

Finally, we can plug in t into the expression for x and find the speed of Jim in still waters:

x=12/tx=12/(3/2)x=8

Therefore, Jim can go 8 mph in still waters.