The Connecticut River flows at a rate of 5 km / hour for the length of a popular scenic route. If a cruiser to travels 4 hours with the current to reach a drop-off point, but the return trip against the same current took 6 hours. Find the speed of the boat without a current?
The speed of the boat without a current is___
since distance = speed * time,
4(s+5) = 6(s-5)
Oh, buoy! Let's paddle through this question together. If the Connecticut River flows at a rate of 5 km/h, and it took 4 hours to go downstream (with the current) and 6 hours to go upstream (against the current), we can figure this waterway conundrum out.
Let's suppose the speed of the boat without a current is "B" km/h. When traveling downstream, the boat's speed is (B + 5) km/h (since it gets an extra boost from the current), and when traveling upstream, the boat's speed is (B - 5) km/h (as it has a current working against it).
Now, using the good ol' distance formula (distance = speed × time), we can set up two equations to solve for B:
For the downstream trip: Distance = Speed × Time
Distance = (B + 5) km/h × 4 hours
And for the upstream trip: Distance = Speed × Time
Distance = (B - 5) km/h × 6 hours
Since the distance covered in both cases is the same (it's a round trip, after all), we can set these two equations equal to each other:
(B + 5) km/h × 4 hours = (B - 5) km/h × 6 hours
Now we solve for B, the speed of the boat without a current:
4B + 20 = 6B - 30
20 + 30 = 6B - 4B
50 = 2B
B = 25 km/h
So, without a current clowning around, the speed of the boat is 25 km/h!
To find the speed of the boat without a current, we can use the concept of relative speed.
Let's assume the speed of the boat without a current is "x" km/h.
When the boat is moving downstream with the current, its effective speed is the sum of its own speed and the speed of the current. In this case, the effective speed is (x + 5) km/h.
For the downstream journey, the boat travels for 4 hours, so the distance covered is (x + 5) * 4 km.
Similarly, when the boat is moving upstream against the current, its effective speed is the difference between its own speed and the speed of the current. In this case, the effective speed is (x - 5) km/h.
For the upstream journey, the boat travels for 6 hours, so the distance covered is (x - 5) * 6 km.
Since the distance covered for both journeys is the same (as it is a round trip), we can set up the following equation:
(x + 5) * 4 = (x - 5) * 6
Now let's solve the equation:
4x + 20 = 6x - 30
2x = 50
x = 25
Therefore, the speed of the boat without a current is 25 km/h.
To find the speed of the boat without a current, we need to use the concept of relative velocity.
Let's assume the speed of the boat without a current is x km/hr.
When the boat is traveling downstream with the current, the effective speed is the sum of the boat's speed and the current's speed. So, the effective speed is (x + 5) km/hr.
Given that it took 4 hours for the boat to travel downstream with the current, we can set up the following equation:
Distance = Speed × Time
=> Distance = (x + 5) × 4
Now, let's consider the return trip where the boat is traveling upstream against the current. In this case, the effective speed is the difference between the boat's speed and the current's speed. So, the effective speed is (x - 5) km/hr.
Given that it took 6 hours for the boat to travel upstream against the current, we can set up the following equation:
Distance = Speed × Time
=> Distance = (x - 5) × 6
Since the distance traveled in both cases is the same, we can equate the two equations:
(x + 5) × 4 = (x - 5) × 6
Now, let's solve this equation:
4x + 20 = 6x - 30
2x = 50
x = 25
Therefore, the speed of the boat without a current is 25 km/hr.