The speed of the current is 4 miles per hour.
It is given that,
- A powerboat takes some 30 mins to travel 10 miles downstream.
- The return trip takes 50 mins.
Explanation:
The formula for speed is:
[tex]Speed=\dfrac{Distance}{Time}[/tex]
We know that 30 mins is equal to 0.5 hour. She speed of the boat in downstream is:
[tex]s_1=\dfrac{10}{0.5}[/tex]
[tex]s_1=20[/tex] mph
We know that 50 mins is equal to [tex]\dfrac{5}{6}[/tex] hour. She speed of the boat in upstream is:
[tex]s_2=\dfrac{10}{\frac{5}{6}}[/tex]
[tex]s_2=12[/tex] mph
Let [tex]b[/tex] be the speed of the boat in still water and [tex]c[/tex] be the speed of the current. Then,
[tex]b+c=20[/tex] ...(i)
[tex]b-c=12[/tex] ...(ii)
Adding (i) and (ii), we get
[tex]2b=32[/tex]
[tex]b=16[/tex]
Substitute [tex]b=16[/tex] in (i).
[tex]16+c=20[/tex]
[tex]c=20-16[/tex]
[tex]c=4[/tex]
The speed of the current is 4 miles per hour.
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