Answer:
Boat speed = 75 miles/ h
Current speed = 25 miles/ h
Step-by-step explanation:
Remember that:
[tex]s = \frac{d}{t}[/tex]
Where
s is the speed
d is the distance
t is the time.
If we call s the speed of the boat and we call c the speed of the current, then we have to:
Boat speed downstream (Boat speed in the same direction as river speed):
[tex](s + c) = \frac{d}{t_1}[/tex]
Where:
[tex]d = 500\ miles[/tex]
[tex]t_1 = 5\ h[/tex]
[tex]s + c = \frac{500}{5}\\\\s + c = 100[/tex]
Boat speed upstream (Boat speed in the opposite direction than the river speed):
[tex](s-c) = \frac{d}{t_2}[/tex]
Where:
[tex]d = 500\ miles[/tex]
[tex]t_2 = 10\ h\\\\s-c = \frac{500}{10}\\\\s-c = 50[/tex]
Then we have the following system of equations:
[tex]s + c = 100[/tex] (1)
[tex]s-c = 50[/tex] (2)
Add equation (1) with equation (2) and solve for s:
[tex]2s = 150\\\\s = 75[/tex]
Now substitute s in equation (2) and solve for c
[tex]75 - c = 50\\\\c = 75-50\\\\c = 25[/tex]
Finally
Boat speed = 75 miles/ h
River speed = 25 miles/ h
