SOLUTION: a boatman goes 96 km in 8 hours with the flow of a river and returns in 12 hours (against the flow). what Will be the respective speed of the boat and the river (in km/hour)?

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Question 733604: a boatman goes 96 km in 8 hours with the flow of a river and returns in 12 hours (against the flow). what Will be the respective speed of the boat and the river (in km/hour)?
Found 3 solutions by lynnlo, ikleyn, greenestamps:
Answer by lynnlo(4176)   (Show Source): You can put this solution on YOUR website!
48KM/4HR.
Answer by ikleyn(53427)   (Show Source): You can put this solution on YOUR website!
.
a boatman goes 96 km in 8 hours with the flow of a river and returns in 12 hours (against the flow).
what will be the respective speed of the boat and the river (in km/hour)?
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let u be the speed of the boat at no current (in kilometers per hour),
and let v be the rate of the current.


The speed of the boat with    the current is  96/8 = 12 km/h.

The speed of the boat against the current is  96/12 = 8 km/h.


The speed of the boat with    the current is  (u + v)  km/h.

The speed of the boat against the current is  (u - v)  km/h.


So, we have these equations

    u + v = 12,    (1)

    u - v =  8.    (2)


By adding equations (1) and (2),               we get  2u = 12 + 8 = 20;  hence,  u = 20/2 = 10 km/h.

By subtracting equation (2) from equation (1), we get  2v = 12 - 8 =  4;  hence,  v = 4/2 = 2 km/h.


ANSWER.  The speed of the boat at no current is 10km/h.

         The rate of the current is 2 km/h.

Solved.

The answers in the post by @lynnlo are incorrect.



Answer by greenestamps(13258)   (Show Source): You can put this solution on YOUR website!


The response from the other tutor shows a typical formal algebraic solution -- which the student certainly should understand.

There are occasions where a quick mental solution is advantageous -- as in a timed competitive exam.

Furthermore, solving the problem informally is good brain exercise.

Going with the current, the boat goes 96 km in 8 hours, so its speed with the current is 96/8 = 12 km/hr.
Going against the current, the boat goes 96 km in 12 hours, so its speed against the current is 96/12 = 8 km/hr.

So ADDing the speed of the current to the speed of the boat gives a speed of 12 km/hr, while SUBTRACTing the speed of the current from the speed of the boat gives a speed of 8 km/hr.

Logical reasoning then tells us that the speed of the boat is halfway between those two speeds, which is 10 km/hr; and that makes the speed of the current 2 km/hr.

ANSWERS: boat speed 10 km/hr; current speed 2 km/hr
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