SOLUTION: A motorboat traveling a distance of 150 miles in 3 hours while traveling with the current. Against the current, the same trip took 5 hours. Find the rate of the boat in calm water
Question 1200814: A motorboat traveling a distance of 150 miles in 3 hours while traveling with the current. Against the current, the same trip took 5 hours. Find the rate of the boat in calm water and the rate of the current.
rate of boat
_____mph
rate of current
______mph Found 2 solutions by math_tutor2020, greenestamps:Answer by math_tutor2020(3816) (Show Source):
Fill in the given distance (150 miles) and the mentioned time values in their correct corresponding slots.
Distance (miles)
Rate (mph)
Time (hours)
With Current
150
3
Against Current
150
5
Then use the formula
rate = distance/time
to get the following
Distance (miles)
Rate (mph)
Time (hours)
With Current
150
50
3
Against Current
150
30
5
Eg:
rate = distance/time = 150/3 = 50 for the "with current" row.
b = speed of boat in still water
c = speed of the current
b+c = 50 ... downstream, i.e. with current
b-c = 30 ... upstream, i.e. against current
Add the equations straight down to eliminate variable c.
2b = 80
b = 80/2
b = 40
notice that 40 mph is the midpoint of 30 mph and 50 mph
Let's determine c based on b = 40
b+c = 50
40+c = 50
c = 50-40
c = 10
Or
b-c = 30
40-c = 30
-c = 30-40
-c = -10
c = 10
Technically you only would need to solve one of those to find c, but it doesn't hurt to have more practice solving both.
It helps to verify the answer is correct.
Answers:
speed of the boat in still water = 40 mph
speed of the current = 10 mph
Another tutor has provided a very long response showing a formal algebraic solution. A formal algebraic solution that fully explains the solution method can be made much shorter.
But this kind of problem is very common, and it can be solved very quickly informally using logical reasoning and (since the numbers are "nice") simple mental arithmetic.
The speed with the current is 150/3 = 50 mph; the speed against the current is 150/5 = 30 mph.
The speed with the current is the boat speed PLUS the speed of the current; the speed against the current is the boat speed MINUS the speed of the current.
Logical reasoning then says that the boat speed is halfway between 50 mph and 30 mph. So the speed of the boat is 40 mph; then the speed of the current is the difference between 40 mph and 50 mph, or between 40 mph and 30 mph.
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