A motor boat took 4 hours to make a downstream trip with a current of 3mph. The return trip against the same current took 8 hours. Find the speed of the boat in still water.
Call Y the boat's rate.
distance = rate x time.
downstream rate of boat is Y+3. t=4 hrs.
upstream rate of boat is Y - 3. t=8 hrs.
d(downstream) = (Y+3)4
d(upstream) = (Y-3)8
The distance is the same so set them equal to each other and solve for Y.
Thank you
9mph
A cruise boat travels 96 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream.
You're on the right track! Let's continue solving the problem.
Set the two distances equal to each other:
(Y + 3) * 4 = (Y - 3) * 8
Now expand and simplify:
4Y + 12 = 8Y - 24
Combine like terms:
12 + 24 = 8Y - 4Y
36 = 4Y
Finally, divide both sides by 4 to solve for Y:
36/4 = 4Y/4
9 = Y
Therefore, the speed of the boat in still water is 9 mph.
If you have any other questions, feel free to ask!
You're welcome! To solve for the speed of the boat in still water, we need to set the distance traveled downstream equal to the distance traveled upstream.
The formula for distance is rate times time. So, the distance traveled downstream is (Y+3) * 4, and the distance traveled upstream is (Y-3) * 8.
Setting these two distances equal to each other, we get:
(Y+3) * 4 = (Y-3) * 8
Now, let's expand and simplify:
4Y + 12 = 8Y - 24
Next, let's combine like terms by subtracting 4Y from both sides:
12 = 4Y - 24
Now, let's add 24 to both sides:
36 = 4Y
Finally, let's divide both sides by 4 to solve for Y:
Y = 9
So, the speed of the boat in still water is 9 mph.
I hope this explanation helps you understand how to solve this type of problem!