In still water, a boat averages 12 miles per hour. It takes the same amount of time to travel 14 miles downstream, with the current , as it does 7 miles upstream, against the current. What is the rate of the water's current?
Down stream = Speed will be added
Up stream = Speed will be reduced
14/(12 + c) = 7/(12 - c) . ............ multiply all by 12
14 (12-c) = 7 (12 + c)
168 - 14 c = 84 + 7c
84 = 21 c
c = 4 miles/second
Answer:
Rate of water's current = 36 miles per hour
Step-by-step explanation:
Let C be the speed of water current
Speed of still water is 12 miles per hour
We know time = distance/ speed
Down stream:
Speed on downstream =C+12
distance travelled = 14 miles
Time =\(\frac{14}{C+12}\)
Upstream
Speed on upstream= C-12
distance travelled = 7 miles
Time =\(\frac{7}{C-12}\)
Time taken for both upstream and down stream are equal . so equate each other and solve for C
\(\frac{14}{C+12}=\frac{7}{C-12}\)
cross multiply it
\(14(C-12)=7(C+12)\)
\(14C-168=7C+84\)
Subtract 7C from both sides
\(7C-168=84\)
Add 168 on both sides
\(7C=252\)
Divide both sides by 7
C= 36
Rate of water's current = 36 miles per hour