A boat travels 30 miles upstream in 4 hours. The trip downstream takes 2.5 hours. Find the rate of he boat in still water.
30 / 4 = 7.5 mph - the boat's speed upstream
30 2.5 = 12 mph - the boat's speed downstream
12 - 7.5 = 4.5 mph - the speed of the current both ways
4.5 / 2 = 2.25 mph - The actual speed of the current.
7.5 + 2.25 =9.75 mph - the speed of the boat in still water, which is the same as:
12 - 2.25 =9.75 mph
+129852 We have that D/T = R
Let the speed in still water be S and let the current speed = C
So....the rate with the current is S + C and the rate going against the current is S - C
And we know that
30/ 2.5 = S + C
12 = S + C (1) and
30/4 = (S - C)
7.5 + C = S (2)
Put (2) into (1)
12 = 7.5 + C + C
12 = 7.5 + 2C
4.5 = 2C divide both sides by 2
2.25 mph = C = rate of the current
And, using (2), the speed of the boat in still water = 7.5 + 2.25 = 9.75mph
