SOLUTION: A motorboat at full throttle takes two hours longer to travel 75 miles against the current than it takes to travel the same distance with current. If the rate of the current is 5 m

Question 191432: A motorboat at full throttle takes two hours longer to travel 75 miles against the current than it takes to travel the same distance with current. If the rate of the current is 5 mph, then what is the speed of the boat at full throttle in still water?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
A) 75=(x-5)*(t+2)
b) 75=(x+5)*(t)

a=b ) x*t+5t=x*t + 2*x - 5*t -10

5*t = -5*t + 2*x -10
5*t + 5*t = 2*x -10
10 *t +10 = 2* x

5*t +5 = x
subst in ( b ) 75 = (( 5*t+5)+(5)) *t
75 = ( 5*t+10) *t

0= 5*t^2 + 10*t - 75
0 = ( 5*t = 25 ) * ( t-3)
t= -5 Not Real and t= +3
subst 5*3 +5 = x
x = 20 ANSWER

check 75 = ( 20-5) * (3+2) = 15 * 5 = 75 ok
check 75 = ( 20 + 5) * (3) = 25 * 3 = 75 ok
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