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Sagot :
Given:
Number of hours, t = 14 hours
Distance = 52 miles
Speed travelling = 8 mph
Let's find the speed of the current.
Apply the formula:
[tex]\begin{gathered} \text{ speed=}\frac{distnace}{time} \\ \\ time=\frac{distance}{speed} \end{gathered}[/tex]Here, we have the system of equations:
For time travelling up: 14 = 52/8-c
For time travelling down: 14 = 52/8 + c
Where c is the speed of the current.
Hence, we have:
[tex]\frac{52}{8-c}+\frac{52}{8+c}=14[/tex]Let's solve the equation for c.
Multiply all terms by (8-c)(8+c):
[tex]\begin{gathered} \frac{52}{8-c}(8-c)(8+c)+\frac{52}{8+c}(8-c)(8+c)=14(8-c)(c+c) \\ \\ 52(8+c)+52(8-c)=14(8-c)(8+c) \end{gathered}[/tex]Solving further, expand using FOIL method and apply distributive property:
[tex]\begin{gathered} 52(8)+52c+52(8)-52c=14(64-c^2) \\ \\ 416+52c+416-52c=896-14c^2 \\ \\ 416+416+52c-52c=896-14c^2 \\ \\ 832-896=-14c^2 \\ \\ -64=-14c^2 \end{gathered}[/tex]Solving further:
Divide both sides by -14
[tex]\begin{gathered} \frac{-64}{-14}=\frac{-14c^2}{-14} \\ \\ 4.57=c^2 \\ \\ c^2=4.57 \\ \\ \text{ Take the square root of both sides:} \\ \sqrt{c^2}=\sqrt{4.57} \\ \\ c=2.14 \end{gathered}[/tex]Therefore, the speed of the current was 2.14 miles per hour.
ANSWER:
2.14 mph
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