Neegan's Paddling Speed in Still Water

Calculating Neegan's Paddling Speed in Still Water

Neegan paddles a kayak 21 miles upstream in 4.2 hours. The return trip downstream takes him 3 hours. What is the rate that Neegan paddles in still water? What is the rate of the current?

Speed of still water = 6 miles/hr
Speed of current = 1 mile/hr
Let,
speed in still water = x mile/hr
speed of current = y mile/hr

Distance = 21 miles

In upstream, speed = (x-y) mile/hr
time = 4.2 hours

In downstream, speed = (x + y) mile/hr
time = 3 hours

We know that,
Distance = speed × time

Therefore, (x - y) × 4.2 = 21
⇒ (x - y) = 5

And, (x + y) × 3 = 21
⇒ (x + y) = 7

Add the equations (1) and (2)
(x - y) + (x + y) = 5 + 7
⇒ 2x = 12
⇒ x = 6

Putting the value of x in equation (2),
6 + y = 7
⇒ y = 7 - 6
⇒ y = 1

So, Neegan's speed in still water = 6 miles/hr
The speed of the current = 1 mile/hr