Question 1011841
.
A boat travelling upstream goes 140 kilometers in 7 hours. If the return trip takes 5 hours, what is the speed (in kilometers per hour) of the boat in still water?
----------------------------------------------------------------------

<pre>
Let u be the boat speed in still water ( in {{{km/h}}} ), and let v be the current speed ( in {{{km/h}}} ).
Then you have two equations


7*(u-v) = 140,    (1)    and
5*(u+v) = 140.    (2)

Indeed, u-v is the boat's speed relatively the river's bank when it is traveling upstream, and
u+ v is the boat's speed relatively the river's bank when it is traveling downstream.

From (1) and (2) you have 

u - v = {{{140/7}}} = 20,   (1')     and
u + v = {{{140/5}}} = 28.   (2')

Now add (1') and (2'). You will get 2u = 20 + 28 = 48. Hence, u = {{{48/2}}} = 24 {{{km/h}}}.

Then from (1') v = u - 20 = 24 - 20 = 4 {{{km/h}}}.

<U>Answer</U>. The speed of the boat in still water is 24 {{{km/h}}}.
</pre>