a tugboat goes 120 miles up streem in 15 hours it takes 10 hours to come back
the speed of the tugboat is and the speed of the curent is
To find the speed of the tugboat and the speed of the current, we can use the concept of relative motion.
Let's assume that the speed of the tugboat is represented by "TB" and the speed of the current by "C."
When the tugboat is traveling upstream (against the current), its effective speed is reduced by the speed of the current. So, the effective speed of the tugboat when traveling upstream is TB - C.
Given that the distance traveled upstream is 120 miles in 15 hours, we can set up the equation:
distance = speed × time
120 = (TB - C) × 15
Simplifying the equation, we have:
8 = TB - C ---(Equation 1)
Similarly, when the tugboat is traveling downstream (with the current), its effective speed is increased by the speed of the current. So, the effective speed of the tugboat when traveling downstream is TB + C.
Given that the distance traveled downstream is 120 miles, and it takes 10 hours, we can set up the equation:
distance = speed × time
120 = (TB + C) × 10
Simplifying the equation, we have:
12 = TB + C ---(Equation 2)
Now, we have two simultaneous equations:
8 = TB - C ---(Equation 1)
12 = TB + C ---(Equation 2)
To solve this system of equations, we can add Equation 1 and Equation 2:
8 + 12 = (TB - C) + (TB + C)
20 = 2TB
Dividing both sides by 2, we get:
TB = 10
Now, we can substitute the value of TB in either Equation 1 or Equation 2 to find the speed of the current. Let's use Equation 1:
8 = 10 - C
Rearranging the equation to solve for C, we have:
C = 10 - 8
C = 2
Therefore, the speed of the tugboat is 10 mph and the speed of the current is 2 mph.