James is kayaking. He can row 3 mph in still water. If he can travel 6 miles downstream in the same amount of time that he can travel 4 miles upstream, what is the speed of the current?

the speed of the current is 0.6 mph

Step-by-step explanation:

Let x represent the speed of the current.

James is kayaking. He can row 3 mph in still water. If he can travel 6 miles downstream. Assuming he went with the current, it means that his total speed while travelling downstream is (3 + x)

Time = distance/speed

Time taken to travel downstream is

6/(3 + x)

In the same amount of time, he can travel 4 miles upstream. Assuming he went against the current, it means that his total speed while travelling downstream is (3 - x). Time taken to travel upstream is

4/(3 - x)

Since the time is the same, then

6/(3 + x) = 4/(3 - x)

Cross multiplying, it becomes

6(3 - x) = 4(3 + x)

18 - 6x = 12 + 4x

4x + 6x = 18 - 12

10x = 6

x = 6/10

x = 0.6 mph

In this case, you aren't going to get an integer for the value of a, but you can rearrange the equation to equal a.

4a-3=D       add 3 to both sides
4a=D+3      divide both sides by 4
a=(D+3)/4   here's your answer