Question 498893: In still water, a boat averages 15 miles per hour. It takes the same amount of time to travel 8 miles downstream, with the current, as 4 miles upstream, against the current. What is the rate of the water's current?
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! You will need to use the equation D=vt for this question, where D=distance, v=velocity (or speed) and t=time.
Let's isolate for time:
t = D/v
and list everything we know (where b stands for boat, w stands for water, d stands for downstream and u stands for upstream):
Vb= 15 mph
Dd = 8 miles
Du = 4 miles
Vd = 15+Vw
Vu = 15-Vw
Note that when you're travelling downstream with the current, you add the boat and water speed together. When you're travelling upstream against the current, you subtract.
We know that t=D/v, and we know that tu = td, so:
Dd/Vd = Du/Vu
8/(15+Vw) = 4/(15-Vw)
Cross-multiply to solve for Vw:
8(15-Vw) = 4(15+Vw)
120-8Vw = 60+4Vw
60 = 12Vw
Vw = 60/12
Vw = 5
The speed of the water is 5 mph.
Hope that helps!
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