A motorboat traveling a distance of 225 miles in 5 hours while traveling with the current. Against the current, the same trip took 9 hours. Find the rate of the boat in calm water and the rate of the current.
rate of boat mph
rate of current mph
Let c=current speed, and
b=boat speed in still water.
Speed with current = 225/5=45 mph
Speed against current = 225/9=25 mph,
Set up equations:
b+c=45
b-c=25
Solve for b and c.
By the way, when you know the sum and difference of two variables, the variable with the larger value equals (sum+difference)/2 and the variable with the smaller value is (sum-difference)/2.
No need to solve for a system of equations.
To find the rate of the boat in calm water and the rate of the current, we can use the formula:
Rate of boat in calm water = (Distance / Time) - Rate of current
Let's start by calculating the rate of the boat with the current. We are given that the boat traveled a distance of 225 miles in 5 hours. So, the rate of the boat with the current can be calculated as:
Rate of boat with current = Distance / Time
= 225 miles / 5 hours
= 45 mph
Now, let's calculate the rate of the boat against the current. The same trip took 9 hours, so:
Rate of boat against current = Distance / Time
= 225 miles / 9 hours
= 25 mph
We can use these two pieces of information to solve for the rate of the boat in calm water and the rate of the current.
Let's assume the rate of the boat in calm water is B mph and the rate of the current is C mph.
Since the rate of the boat with the current is (B + C) mph, we have:
(B + C) mph = 45 mph
Similarly, the rate of the boat against the current is (B - C) mph, so:
(B - C) mph = 25 mph
Now, we can solve this system of equations to find the values of B and C.
Adding the two equations:
(B + C) mph + (B - C) mph = 45 mph + 25 mph
2B mph = 70 mph
Dividing both sides by 2 gives:
B mph = 70 mph / 2
B mph = 35 mph
Now that we know the rate of the boat in calm water (B mph = 35 mph), we can substitute this value back into one of the initial equations to find the rate of the current (C mph):
(B + C) mph = 45 mph
(35 mph + C mph) = 45 mph
Subtracting 35 mph from both sides:
C mph = 45 mph - 35 mph
C mph = 10 mph
Therefore, the rate of the boat in calm water is 35 mph and the rate of the current is 10 mph.