Answer:
b.6 mph
Explanation:
We use the equation s = d/t to solve this.
We do not know Samantha's speed, but we know that going downstream, she swims the given distance in 12 minutes. Going downstream, we add the river's speed, 4, to her speed; this gives us
s+4 = d/12
Solving for d, we will multiply both sides by 12:
12(s+4) = (d/12)(12)
12(s+4) = d
Use the distributive property:
12(s)+12(4) = d
12s+48 = d
Going upstream, Samantha swims the given distance in an hour, 60 minutes. Going upstream, we subtract the river's speed, 4, from her speed; this gives us
s-4 = d/60
Solving for d, we will multiply both sides by 60:
60(s-4) = (d/60)(60)
60(s-4) = d
Use the distributive property:
60(s)-60(4) = d
60s-240 = d
Since both equations equal d, we can set them equal to one another:
12s+48 = 60s-240
Subtract 12s from each side:
12s+48-12s = 60s-240-12s
48 = 48s-240
Add 240 to each side:
48+240 = 48s-240+240
288 = 48s
Divide both sides by 48:
288/48 = 48s/48
6 = s
Samantha's speed is 6 mph.