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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.

Guest Mar 5, 2017
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#1
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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

Guest Mar 5, 2017
#2
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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

CPhill  Mar 5, 2017
#3
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Omg thank you so much Cpill and other guest that helped a lot

Guest Mar 5, 2017
#4
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XD cpill, the druggie black sheep brother of CPhill

MEAT_DUCK117  Mar 6, 2017