An octopus can swim v km/h in still water. When the octopus swims against a current of 5km/h, its speed is decreased by 5km/h. When it swims with a current of 5km/h, its speed it increased by 5km/h. It takes Joey the Octopus the same amount of time to swim 10km with the current as it takes him to swim 8km against the current.

What is Joey the Octopus’ speed in still water?

since time = distance/speed,

10/(v+5) = 8/(v-5)

45 km/h

Let's assume the octopus' speed in still water is "x" km/h.

When swimming against the current, the effective speed would be (x - 5) km/h.
When swimming with the current, the effective speed would be (x + 5) km/h.

We are given that it takes the same amount of time for Joey to swim 10km with the current as it takes him to swim 8km against the current.

Using the formula: time = distance / speed, we can set up the following equation:

10 / (x + 5) = 8 / (x - 5)

Cross multiplying, we get:

10(x - 5) = 8(x + 5)

Expanding, we get:

10x - 50 = 8x + 40

Bringing like terms to one side, we get:

10x - 8x = 40 + 50

Simplifying, we get:

2x = 90

Dividing both sides by 2, we get:

x = 45

Therefore, Joey the Octopus' speed in still water is 45 km/h.

To find Joey the Octopus' speed in still water, we can use the equation for speed, which is distance divided by time:

Speed = Distance / Time

Let's start by determining the time it takes for Joey to swim 10km with the current. We know that his speed increases by 5km/h when swimming with the current, so his speed with the current is (v + 5) km/h.

We can plug this value into the equation to find the time:

Time = Distance / Speed

Time = 10 km / (v + 5) km/h

Similarly, we can determine the time it takes for Joey to swim 8km against the current. We know that his speed decreases by 5km/h when swimming against the current, so his speed against the current is (v - 5) km/h.

Using the same equation for time:

Time = Distance / Speed

Time = 8 km / (v - 5) km/h

According to the problem, these times are equal:

10 km / (v + 5) km/h = 8 km / (v - 5) km/h

To solve this equation, we can cross multiply:

10(v - 5) = 8(v + 5)

10v - 50 = 8v + 40

Subtract 8v from both sides:

2v - 50 = 40

Add 50 to both sides:

2v = 90

Divide by 2:

v = 45

Therefore, Joey the Octopus' speed in still water is 45 km/h.