Question

The speed of a boat in still water is 25 mph. The Jacksons traveled 70 ml down the Woodset River in this boat in the same amount of time it took them to return 30 mi up the river. Find the rate of the river's current?

Answer 1

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 = $x$ mph

Speed of the boat down the river = $x+25$ mph

Speed of the boat up the river = $25-x$ mph

$Time=\frac{Distance}{speed}$

$t_{down}=\frac {70}{x+25}$ hours  [$t_{down}$ represent tie taken by the boat down stream.]

$t_{up}=\frac{30} {25-x}$ hours [$t_{up}$ represent tie taken by the boat up stream.]

We know that $t_{down}=t_{up}$

So, $\frac {70}{x+25}=\frac{30} {25-x}$

Solving for $x$

Cross multiplication.

$70(25-x)=30(x+25)$

Using distribution.

$(70(25)-70x)=(30x+30(25))\\1750-70x=30x+750$

Adding $70x$ both sides.

$1750-70x+70x=30x+750+70x$

$1750=100x+750$

Subtracting $750$ fro both sides.

$1750-750=100x+750-750$

$1000=100x$

Dividing both sides by $100$

$\frac{1000}{100}=\frac{100x}{100}$

∴ $x=10$

Speed of river's current = 10 mph