Samantha swam upstream for some distance in one hour. she then swam downstream the same river for the same distance in only 12 minutes. if the river flows at 4 mph, how fast can samantha swim in still water? a.3 mph b.6 mph c.7 mph d.8 mph

b.6 mph  

Step-by-step 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.

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