2. The excursion boat Holiday travels 35km upstream and then back again in 4h 48min. If the speed of the Holiday in still water is 15km/h, what is the speed of the current?

speed of current ---- x km/h

speed against current --- 15-x
speed with current ----- 15+x

time against current = 35/(15-x)
time with current = 35/(15+x)

so solve
35/(15-x) + 35/(15+x) = 4.8

(I suggest multiplying each term by (5+x)(15-x), you will end up with a quadratic equation )

To solve this problem, we can use the formula for calculating the time taken for a journey at a given speed.

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

When the boat is traveling upstream, its effective speed is reduced by the speed of the current, so its speed is 15 - c km/h.

When the boat is traveling downstream, its effective speed is increased by the speed of the current, so its speed is 15 + c km/h.

Given that the total time taken for the excursion is 4 hours and 48 minutes, which is equal to 4 + 48/60 = 4.8 hours.

The total distance traveled is twice the distance traveled upstream or downstream, which is 2 * 35 = 70 km.

Now, let's calculate the time taken for the upstream journey:

Time taken = Distance / Speed
Time taken upstream = 35 / (15 - c)

And, the time taken for the downstream journey:

Time taken downstream = 35 / (15 + c)

The total time taken for the whole excursion is the sum of the times taken for the upstream and downstream journeys:

4.8 = 35 / (15 - c) + 35 / (15 + c)

To simplify the equation, let's multiply both sides by (15 - c)(15 + c):

4.8 * (15 - c)(15 + c) = 35(15 + c) + 35(15 - c)

Now, let's simplify the equation:

4.8(225 - c^2) = 35(15 + c) + 35(15 - c)
1080 - 4.8c^2 = 525 + 35c + 525 - 35c
1080 - 4.8c^2 = 1050

Now, let's solve for 'c':

4.8c^2 = 30
c^2 = 30 / 4.8
c^2 = 6.25
c = √6.25

Therefore, the speed of the current is approximately 2.5 km/h.

To find the speed of the current, we need to understand the relationship between the speed of the boat in still water, the speed of the current, and the time it takes to travel a certain distance.

Let's denote the speed of the boat in still water as "b" and the speed of the current as "c."

When the boat is traveling upstream (against the current), the effective speed is reduced by the speed of the current. So the speed of the boat going upstream is (b - c).

When the boat is traveling downstream (with the current), the effective speed is increased by the speed of the current. So the speed of the boat going downstream is (b + c).

Now, let's analyze the given information. The boat travels a total distance of 35 km upstream and then back again.

The time it takes to travel a certain distance can be calculated using the formula: Time = Distance/Speed.

When the boat is traveling upstream, the time it takes is 35/(b - c) because the speed is reduced by the current.

When the boat is traveling downstream, the time it takes is 35/(b + c) because the speed is increased by the current.

According to the problem, the total time it takes for the round trip is 4 hours and 48 minutes, which can be converted to 4.8 hours.

So, we can set up the equation:

35/(b - c) + 35/(b + c) = 4.8

Now we need to solve this equation to find the value of "c."

To solve this equation, we can simplify the equation by cross-multiplying and combining like terms:

35(b + c) + 35(b - c) = 4.8(b - c)(b + c)

Simplifying further:

35b + 35c + 35b - 35c = 4.8(b^2 - c^2)

70b = 4.8b^2 - 4.8c^2

Rearranging the equation:

4.8c^2 + 4.8b^2 - 70b = 0

Now we have a quadratic equation that can be solved to find the value of "c." We can use the quadratic formula to solve this equation.