Cody’s motorboat took 3 hr to make a trip downstream with a 6-mph current. The return trip against the same current took 5 hr. Find the speed of the boat in still water
Time= distance*velocity
3=d*(vb+vs)
5=d(Vb-vs)
3/d= vb+Vs
5/d=Vb-Vs
add the equations
3/d + 5/d=2Vb
5d+3d=30Vb
solve for Vb
speed of boat in still water ---- x mph
distance going upstream = 5(x-6)
distance going downstream = 3(x+6)
Are the distances not equal ?
To find the speed of the boat in still water, we need to use the concept of relative motion.
Let's assume that the speed of the boat in still water is 'b' mph.
When the boat is going downstream, it moves with the current. Therefore, its effective speed is the sum of the speed of the boat in still water and the speed of the current:
Effective speed downstream = b + 6 mph
Given that it takes 3 hours to make the downstream trip, we can use the formula: Speed = Distance / Time
Distance downstream = (b + 6) mph * 3 hours
Similarly, when the boat is going upstream, it moves against the current. Therefore, its effective speed is the difference between the speed of the boat in still water and the speed of the current:
Effective speed upstream = b - 6 mph
Given that it takes 5 hours to make the upstream trip, we can again use the formula: Speed = Distance / Time
Distance upstream = (b - 6) mph * 5 hours
Now, since the distance traveled downstream is the same as the distance traveled upstream, we can equate the two distances:
(b + 6) mph * 3 hours = (b - 6) mph * 5 hours
Simplifying the equation:
3b + 18 = 5b - 30
2b = 48
b = 24
Therefore, the speed of the boat in still water is 24 mph.