A patrol boat took 2.5 h for a round trip 12 km upriver and 12 km back. The speed of the current 2 km/h. What was the speed of the boat in still water?
Since time = distance/speed, we have
12/(x-2) + 12/(x+2) = 5/2
x=10
check:
12 km upstream at 8 km/hr = 1.5 hr
12 km downstream at 12 km/hr = 1 hr
total tiome: 2.5 hr
aaa
To find the speed of the boat in still water, we can use the formula:
Speed of Boat in Still Water = (Speed Downstream + Speed Upstream) / 2
Let's calculate the speed downstream first:
Speed Downstream = (Distance Downstream) / (Time Downstream)
= (12 km) / (2.5 hours)
= 4.8 km/h
Since the boat is traveling downstream, the speed of the current will add to the speed of the boat, so the effective speed downstream is:
Effective Speed Downstream = Speed Downstream + Speed of Current
= 4.8 km/h + 2 km/h
= 6.8 km/h
Now, let's calculate the speed upstream:
Speed Upstream = (Distance Upstream) / (Time Upstream)
= (12 km) / (2.5 hours)
= 4.8 km/h
Since the boat is traveling upstream, the speed of the current will subtract from the speed of the boat, so the effective speed upstream is:
Effective Speed Upstream = Speed Upstream - Speed of Current
= 4.8 km/h - 2 km/h
= 2.8 km/h
Finally, we can find the speed of the boat in still water using the formula mentioned earlier:
Speed of Boat in Still Water = (Effective Speed Downstream + Effective Speed Upstream) / 2
= (6.8 km/h + 2.8 km/h) / 2
= 4.8 km/h
Therefore, the speed of the boat in still water is 4.8 km/h.
To find the speed of the boat in still water, we can use the concept of relative speed. The relative speed is the difference between the boat's speed in still water and the speed of the current.
Let's assume the speed of the boat in still water is 'B' km/h. Given that the speed of the current is 2 km/h, the boat's speed when going upriver against the current will be (B - 2) km/h. On the return trip downstream, the boat's speed will be (B + 2) km/h.
Now, we know that the total distance traveled upriver and downstream is 12 km each way, and it took 2.5 hours for the round trip.
For the upriver trip, the boat's speed is (B - 2) km/h, and the distance is 12 km. Using the formula speed = distance / time, we can write:
(B - 2) km/h = 12 km / t1
Where t1 is the time taken for the upriver trip.
For the downstream trip, the boat's speed is (B + 2) km/h, and the distance is also 12 km. Using the same formula, we have:
(B + 2) km/h = 12 km / t2
Where t2 is the time taken for the downstream trip.
Since the total time for the round trip is 2.5 hours, we can write:
t1 + t2 = 2.5 hours
Now, we have a system of two equations with two variables:
(B - 2) km/h = 12 km / t1
(B + 2) km/h = 12 km / t2
t1 + t2 = 2.5 hours
We can solve this system of equations to find the value of B, which represents the speed of the boat in still water.
By manipulating and combining the equations, we can find the solution for B.