Respuesta :
Answer:
Speed of river's current = 10 mph
Step-by-step explanation:
Given:
Speed of boat in still water =25 mph
Distance traveled by Jacksons down stream= 70 miles
Distance traveled by Jacksons up stream= 30 miles
Let rate of river's current be = [tex]x[/tex] mph
Speed of the boat down the river = [tex]x+25[/tex] mph
Speed of the boat up the river = [tex]25-x[/tex] mph
[tex]Time=\frac{Distance}{speed}[/tex]
[tex]t_{down}=\frac {70}{x+25}[/tex] hours [[tex]t_{down}[/tex] represent tie taken by the boat down stream.]
[tex]t_{up}=\frac{30} {25-x}[/tex] hours [[tex]t_{up}[/tex] represent tie taken by the boat up stream.]
We know that [tex]t_{down}=t_{up}[/tex]
So, [tex]\frac {70}{x+25}=\frac{30} {25-x}[/tex]
Solving for [tex]x[/tex]
Cross multiplication.
[tex]70(25-x)=30(x+25)[/tex]
Using distribution.
[tex](70(25)-70x)=(30x+30(25))\\1750-70x=30x+750[/tex]
Adding [tex]70x[/tex] both sides.
[tex]1750-70x+70x=30x+750+70x[/tex]
[tex]1750=100x+750[/tex]
Subtracting [tex]750[/tex] fro both sides.
[tex]1750-750=100x+750-750[/tex]
[tex]1000=100x[/tex]
Dividing both sides by [tex]100[/tex]
[tex]\frac{1000}{100}=\frac{100x}{100}[/tex]
∴ [tex]x=10[/tex]
Speed of river's current = 10 mph
