Question

Please help! Naira paddled 4.5 km with the current in the same amount of time as it took her to paddle 3 km against the current. Naira paddled at an average rate of 5 kmh relative to the water each way. Assume the speed of the current was constant.

What was the speed of the current?

Answer 1

The speed of the current is 1 km/h.

Step-by-step explanation:

Let's assume the speed of the current is x km/h.

When Naira paddles with the current, her effective speed is the sum of her paddling speed and the speed of the current.

Therefore, when Naira paddles 4.5 km with the current, her effective speed is 5 + x km/h.

Similarly, when Naira paddles against the current, her effective speed is the difference between her paddling speed and the speed of the current.

Therefore, when Naira paddles 3 km against the current, her effective speed is 5 - x km/h.

Since Naira took the same amount of time for both the distances,

4.5 / (5 + x) = 3 / (5 - x)

Cross multiplying, we get:

4.5 (5 - x) = 3 (5 + x)

Simplifying the equation:

22.5 - 4.5x = 15 + 3x

Bringing all the x terms to the left side:

22.5 - 15 = 4.5x + 3x

7.5 = 7.5x

Dividing by 7.5 on both sides:

x = 1

Therefore, the speed of the current is 1 km/h.

Answer 2

Let's denote the speed of Naira's boat as "v" and the speed of the current as "c".

When Naira paddles with the current, her effective speed is (v + c) km/h.

When she paddles against the current, her effective speed is (v - c) km/h.

We know that Naira paddled 4.5 km with the current in the same amount of time as it took her to paddle 3 km against the current.

Using the formula:

time = distance / speed

We can write two equations based on the given information:

4.5 / (v + c) = 3 / (v - c)

and

(v + c) = 5

We can simplify the first equation by cross-multiplying:

4.5(v - c) = 3(v + c)

Expanding the brackets:

4.5v - 4.5c = 3v + 3c

Combining like terms:

1.5v = 7.5c

Dividing both sides by 1.5:

v = 5c

Substituting v = 5 into the second equation:

5 + c = 5

c = 0

Therefore, the speed of the current is 0 km/h. This means that Naira paddled at a speed of 5 km/h relative to the water both with and against the current.