A speed boat travels at a rate of 20 km per hour in still water. It travels 55 km upstream the same time it travels 90 km downstream. What is the rate of current?

since time = distance/speed,

55/(20-x) = 90/(20+x)

Let's assume the rate of the current is 'x' km per hour.

When the speed boat is traveling upstream (against the current), it faces a relative speed of (20 - x) km per hour, as the current opposes its motion. Therefore, the time taken to travel 55 km upstream is:

Time = Distance / Speed
= 55 / (20 - x)

When the speed boat is traveling downstream (with the current), it gains a relative speed of (20 + x) km per hour, as the current aids its motion. Therefore, the time taken to travel 90 km downstream is:

Time = Distance / Speed
= 90 / (20 + x)

According to the given information, the time taken to travel upstream is the same as the time taken to travel downstream. Hence, we can set up the following equation:

55 / (20 - x) = 90 / (20 + x)

Let's solve this equation to find the value of 'x', the rate of the current.

Cross-multiplying, we get:

55 * (20 + x) = 90 * (20 - x)

Expanding the equation:

1100 + 55x = 1800 - 90x

Combining like terms:

145x = 700

Dividing both sides by 145, we find:

x = 700 / 145
x ≈ 4.82

Therefore, the rate of the current is approximately 4.82 km per hour.

To solve this problem, we can use the formula for the time it takes to travel a given distance:

Time = Distance / Speed

Let's denote the rate of the current as "x" km/h.

When the speed boat is traveling upstream (against the current), the effective speed is reduced by the speed of the current. So, the speed of the boat upstream would be (20 - x) km/h.

When the speed boat is traveling downstream (with the current), the effective speed is increased by the speed of the current. So, the speed of the boat downstream would be (20 + x) km/h.

We are told that the time taken to travel 55 km upstream is the same as the time taken to travel 90 km downstream.

Using the formula mentioned earlier, we can write the equation for the time taken for each leg of the journey:

55 / (20 - x) = 90 / (20 + x)

To solve this equation, we can cross-multiply:

55(20 + x) = 90(20 - x)

Now, let's simplify the equation:

1100 + 55x = 1800 - 90x

Adding 90x to both sides:

145x + 1100 = 1800

Subtracting 1100 from both sides:

145x = 700

Dividing both sides by 145:

x = 700 / 145

Simplifying on a calculator:

x ≈ 4.83

Therefore, the rate of the current is approximately 4.83 km/h.