SOLUTION: a motorboat goes 36 miles upstream on a river whoes current is running at 3 miles per hour. the trip up and back takes 5 hours. what is the speed of the boat (assuming that it nain
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Question 549233: a motorboat goes 36 miles upstream on a river whoes current is running at 3 miles per hour. the trip up and back takes 5 hours. what is the speed of the boat (assuming that it naintains a constant speed relative to the water)?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
boat speed x mph
current speed =3mph
Distance =36 miles
speed with current =x + 3 mph
speed against current x -3 mph
Total time = 5 hours
Time with current= 36/( x + 3 )
time against current 36/( x -3 )
Time with current + time against =5 hours
36/(x+3)+36/(x-3)=5
LCD =(x+3)*(x-3)
multiply the equation by the LCD
we get
36*(x-3)+36(x+3)=5(x^2+0x+9)
36x-108 +36x+108=5X^2-45
72x=5X^2-45
5X^2-72x-45=0
5X^2-72x-45= 0
/ 5
5x^2-72 x-45=0
Find the roots of the equation by quadratic formula
a= 5 ,b= -72 ,c= -45
b^2-4ac= 5184 + 900
b^2-4ac= 6084
=78
x1=(72+78)/10
x1= 15
x2=( 72 -78 ) / 10
x2= -0.60
Ignore negative value
boat speed = 15 mph
m.ananth@hotmail.ca
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