a boat travels 10 miles upstream in 4 hours. the boat travels the same distance downstream in 2 hours. Determine the rate of boat in still water and the rate of the current?
Downstream speed = b(still water) + c(current)
Upstream speed = b - c
upstream rate = 10/4 miles/hr
downstream rate = 10/2 = 5 miles/hr
what to do next? thanks
So,
b-c = 10/4
b+c = 5
To determine the rate of the boat in still water (b) and the rate of the current (c), we can set up a system of equations using the given information.
Let's assign variables to the unknowns:
b = rate of the boat in still water (in miles per hour)
c = rate of the current (in miles per hour)
From the given information, we can set up the following equations:
Equation 1: Downstream speed = b + c
Equation 2: Upstream speed = b - c
Equation 3: Upstream rate = 10/4 miles/hour
Equation 4: Downstream rate = 10/2 miles/hour
Now, let's substitute the values from Equations 3 and 4 into Equations 1 and 2:
Equation 1: 5 = b + c (substituting the downstream rate of 5 miles/hour)
Equation 2: 2.5 = b - c (substituting the upstream rate of 2.5 miles/hour)
Next, we can solve this system of equations to find the values of b and c. We can do this by adding and subtracting these two equations:
Equation 1 + Equation 2: 5 + 2.5 = (b + c) + (b - c)
7.5 = 2b
b = 7.5/2
b = 3.75 miles/hour
Equation 1 - Equation 2: 5 - 2.5 = (b + c) - (b - c)
2.5 = 2c
c = 2.5/2
c = 1.25 miles/hour
Therefore, the rate of the boat in still water (b) is 3.75 miles/hour and the rate of the current (c) is 1.25 miles/hour.