it took 3 hours for patrol boat to travel 48km upstream and 2 hours to travel downstream. What is the current and boat speed.
To find the speed of the boat and the speed of the current, we can use the formula:
Boat speed + Current speed = Downstream speed
Boat speed - Current speed = Upstream speed
Let's assign some variables:
Let's call the boat speed B and the current speed C.
Given that it took 3 hours to travel 48 km upstream and 2 hours to travel downstream, we can set up the following equations:
B - C = 48 km / 3 hours = 16 km/h (Equation 1)
B + C = 48 km / 2 hours = 24 km/h (Equation 2)
Now, we have a system of equations. To solve them, we can use a method called substitution:
From Equation 1, we can solve for B:
B = 16 + C (Equation 3)
Substitute Equation 3 into Equation 2:
(16 + C) + C = 24
16 + 2C = 24
2C = 8
C = 4 km/h
Substitute the value of C back into Equation 3 to find B:
B = 16 + 4
B = 20 km/h
So, the speed of the boat is 20 km/h and the speed of the current is 4 km/h.
c+b=48km/2hrs
b-c=48/3
add the equations
2b=24+16=40
b=20km/hr
you then find a