Respuesta :
Answer:
Current rate of boat is 6.96 mph.
Step-by-step explanation:
Given:
Distance traveled = 48 miles.
Time to travel = 7 hours
Speed of the boat in still water = 12 mph
We need to find the Current rate.
Let current rate be x;
Downstream rate = [tex]12+x[/tex]
Upstream rate = [tex]12-x[/tex]
Now we know that Time is given by dividing Distance with Speed.
Hence Distance traveled is upstream and downstream.
Framing the equation we get;
[tex]\frac{48}{12-x}-\frac{48}{12+x} = 7[/tex]
Now taking LCM we get;
[tex]\frac{48(12+x)-48(12-x)}{(12+x)(12-x)}=7\\\\576+48x-576+48x=7\times (12+x)(12-x)\\96x=7\times(144-x^2)\\96x=1008-7x^2\\7x^2+96x-1008=0[/tex]
Now we will find the roots using quadratic formula.
a = 7 b =96 c =-1008
[tex]b^2-4ac=96^2-4\times7\times-1008\\b^2-4ac=9216+28224 = 37440\\\sqrt{b^2-4ac} = \sqrt{37440} =193.49[/tex]
Now Quadratic formula is given by;
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x_1= \frac{-96+193.49}{2\times7} = 6.96\\\\x_2= \frac{-96-193.49}{2\times7} = -20.67[/tex]
Now we have 2 values of x = 6.96 and x = -20.67
Since Speed of the boat cant be negative.
Hence we can say Current rate of boat is 6.96 mph
