Respuesta :
The speed of the boat in still water is 16 miles per hour. So, the given speed of 0.5 is incorrect.
Let, v = the speed of the boat in still water.
The current of a river is 4 miles per hour.
On going upstream, the boat travels v−4 miles per hour.
On going downstream, the boat travels v+4 miles per hour.
So we can write,
( 30 miles × 1 hour ) / (v − 4 miles) = 30 / ( v − 4 ) hours
( 30 miles × 1 hour ) / ( v + 4 ) miles= 30 / ( v + 4 )hours
a boat travels to a point 30 miles upstream and back in 4 hours. So, on adding equation 1 and equation two we will get 4. Mathematically,
{30 / ( v − 4 )} + {30 / ( v + 4 )} = 4
30 ( v + 4 ) + 30 ( v - 4 ) = 4 ( v - 4 ) ( v + 4 )
60v = 4 ( [tex]v^{2} - 16[/tex] )
4 [tex]v^{2}[/tex] - 60 v - 64 = 0
[tex]v^{2}[/tex] - 15v - 16 = 0
( v - 16 ) (v + 1 ) = 0
v = -1 , 16
speed in still water cannot be negative. So, we can neglect -1 . the speed of the boat in still water is 16 miles per hour.
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