Question

Bob can row 12 mph in still water. The total time to travel downstream and return upstream to the starting point is 4 hours. If the total distance downstream and back is 36 miles, determine the speed of the river (current speed).

Answer 1

Answer:

$\boxed{\sf \ 6 \ mph \ }$

Step-by-step explanation:

when Bob travels downstream his speed is 12 + x

where x is the speed of the river

he travels 36/2 = 18 miles

it takes

   $\dfrac{18}{(12+x)}$

hours to  do it  

when Bob travels upstream his speed is 12 - x

it takes

   $\dfrac{18}{(12-x)}$

hours to  do it  

finally, it takes

   $\dfrac{18}{(12+x)}+\dfrac{18}{(12-x)}=4$

$<=> 18(12-x+12+x)=4(12+x)(12-x)\\\\<=> 18*24=4(12^2-x^2)\\<=> 4x^2=576-432=144\\<=> 2x=12\\ <=> x = 6$

So the current speed is 6mph

it takes 1 hour to downstream and 3 hours to upstream

hope this helps