A motorboat at full throttle takes two hours longer to trave

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?

Solution

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