Answer:
4 mph
Step-by-step explanation:
Let x is the speed of the current
Let y is the speed of the motorboat
As we know: speed = distance / time
It takes 30 minutes (= 1/2 hours) for the boat to go upstream the same 8 miles
y - x = 8 / [tex]\frac{1}{2}[/tex] mph
<=> y - x = 16 mph (1)
<=> x = y -16 mph
A motorboat can go 8 miles downstream on a river in 20 minutes (= 1/3 hour)
y + x = 8 / [tex]\frac{1}{3}[/tex] mph
<=> y + x = 24 mph (2)
Solve the system of equation (1) and (2), we have:
y + x = 24 mph
<=> y + y -16 = 24 mph
<=> 2y = 40 mph
<=> y = 20 mph
=> x = 20 -16 = 4 mph
So the speed of the current is 4 mph
