Question

A kayaker paddles 2 km upstream in the same time that it takes to paddle 3 km downstream. The average speed of the current is 1 km/h. What is the average speed of the kayak in still water?

I need the work as well pleasee!!

Answer 1

To find the kayak's average speed in still water, one must equate the time taken to paddle upstream and downstream, considering the current's speed. With this method, the kayak's average speed in still water is calculated to be 5 km/h.

Step-by-step explanation:

The question is asking for the average speed of the kayak in still water given that a kayaker paddles 2 km upstream and 3 km downstream in the same amount of time with a current speed of 1 km/h. To solve this, we can define the variables Vk as the kayak's speed in still water and Vc=1 km/h as the current's speed.

When the kayak is going upstream, its effective speed is Vk - Vc, and when going downstream, its effective speed is Vk + Vc. Since the times are the same for paddling upstream and downstream, we can set up an equation that equates the time taken for both parts of the trip:

T = 2/(Vk - Vc) = 3/(Vk + Vc)

We substitute Vc as 1 km/h and can start cross multiplying to solve the equation:

• 2(Vk + 1) = 3(Vk - 1)
• 2Vk + 2 = 3Vk - 3
• Vk = 5 km/h

Therefore, the kayak's average speed in still water is 5 km/h.

Answer 2

Let x represent speed of kayak in the still water.

We have been given that a kayaker paddles 2 km upstream in the same time that it takes to paddle 3 km downstream. The average speed of the current is 1 km/h.

Speed of kayak upstream would be speed of kayak in still water minus speed of the current that is
`x-1`.

Speed of kayak downstream would be speed of kayak in still water plus speed of the current that is
`x+1`.

`\text{Time}=\frac{\text{Distance}}{\text{Speed}}`

Time taken to travel 2 km upstream would be
`(2)/(x-1)`.

Time taken to travel 3 km upstream would be
`(3)/(x+1)`.

Since both times are equal, so we can equate both expressions as:

`(3)/(x+1)=(2)/(x-1)`

Cross multiply:

`3(x-1)=2(x+1)`

`3x-3=2x+2`

`3x-2x-3=2x-2x+2`

`x-3=2`

`x-3+3=2+3`

`x=5`

Therefore, the average speed of Kayak in still water is 5 km per hour.