The speed of the boat if it were in still water is 11.25 miles per hour and the speed of the current is 3.75 miles per hour.
According to the question,
We have the following information:
A boat take 4 hour to travel upstream 30 miles. On the return trip downstream it took 2 hours.
Now, let's take the speed of the boat in still water to be s miles per hour and the speed of the current to be c miles per hour.
Upstream speed = speed in still water - speed of current
Downstream speed = speed in still water + speed of current
Upstream:
s-c = 30/4
s-c = 7.5
s = 7.5+c ...(1)
Downstream:
s+c = 30/2
s+c = 15
Putting the value of s from equation 1:
7.5+c+c = 15
7.5+2c = 15
2c = 15-7.5
2c = 7.5
c = 7.5/2
c = 3.75 miles per hour
Putting this value in equation 1:
s = 7.5+c
s = 7.5+3.75
s = 11.25 miles per hour
Hence, the speed of the boat if it were in still water is 11.25 miles per hour and the speed of the current is 3.75 miles per hour.
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