Answer:
3 mph
Step-by-step explanation:
To solve this we are using the kinematic equation [tex]t=\frac{d}{v}[/tex] , where:
[tex]t[/tex] is the time
[tex]d[/tex] is the distance
[tex]v[/tex] is the speed of the current
Since traveling downstream the speed of the boat is going in the same direction as the speed of the current, we add both speeds, so [tex]13+v[/tex]. We also know that Kim traveled 48 miles downstream, so [tex]d=48[/tex]. Replacing values we get [tex]t=\frac{48}{13+v}[/tex] equation (1)
Now, since traveling upstream the boat is going against the current, we subtract the speed from the current from the speed of the boat: [tex]13-v[/tex]. We also know that Kim traveled 30 miles upstream, so [tex]d=30[/tex]. Replacing values we get [tex]t=\frac{30}{13-v}[/tex] equation (2)
Since she traveled 48 miles downstream in the same amount of time that it would take her to row 30 miles upstream, we can replace equation (1) in (2) and solve for [tex]v[/tex]:
[tex]\frac{48}{13+v} =\frac{30}{13-v}[/tex]
Cross-multiply
[tex]48(13-v)=30(13+v)[/tex]
[tex]624-48v=390+30v[/tex]
[tex]624-390=30v+48v[/tex]
[tex]234=78v[/tex]
[tex]v=\frac{234}{78}[/tex]
[tex]v=3[/tex]
We can conclude that the speed of the current is 3 mph.
