A boat can travel 48 miles downstream in 4 hours and can make the return trip in 6 hours. Find the speed of the boat in still water.
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since distance = speed * time
if x is the boat's speed and y is the water's speed, we have
4(x+y) = 48
6(x-y) = 48
Hint: 48 = 4*12 = 6*8
I am having a problem remembering how to word it to solve the problem...
To find the speed of the boat in still water, we can use the concept of relative speed.
Let's assume the speed of the boat in still water is 'b' miles per hour (mph), and the speed of the current (the water flow) is 'c' mph.
When the boat is going downstream, it is moving along with the current, so its effective speed is increased by the speed of the current:
Effective speed downstream = b + c
Conversely, when the boat is going upstream, it is moving against the current, so its effective speed is decreased by the speed of the current:
Effective speed upstream = b - c
According to the given information, the boat can travel 48 miles downstream in 4 hours, which gives us the equation:
48 miles = (b + c) mph × 4 hours
Similarly, the boat can make the return trip (upstream) in 6 hours:
48 miles = (b - c) mph × 6 hours
Now, we have a system of two equations with two variables (b and c). Let's solve these equations to find the speed of the boat in still water.
First, let's simplify the equations:
1) First equation: 48 miles = (b + c) mph × 4 hours
Dividing both sides of the equation by 4 hours, we get:
12 mph = b + c
2) Second equation: 48 miles = (b - c) mph × 6 hours
Dividing both sides of the equation by 6 hours, we get:
8 mph = b - c
Now, we have a system of two linear equations:
12 mph = b + c
8 mph = b - c
We can solve this system of equations using the method of elimination.
Adding the two equations together, we eliminate 'c':
(12 mph) + (8 mph) = (b + c) + (b - c)
20 mph = 2b
Dividing both sides of the equation by 2, we find:
b = 10 mph
The speed of the boat in still water is 10 miles per hour.