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ki77a [65]
3 years ago
8

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).
Mathematics
1 answer:
RSB [31]3 years ago
6 0

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

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