I think the answer is 2 mph in still water and 3mph in the current

## a girl rows a boat 6 miles upstream in 3 hours. she returns 6 miles downstream in 2 hours. how fast does she go each way?

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# 4 Answers

a girl rows a boat 6 miles upstream in 3 hours. she returns 6 miles downstream in 2 hours. how fast does she go each way?

Upstream speed is:

6 miles

--------

3 hours

Dividing numerator and denominator by 3:

2 miles

--------

1 hour

That's 2 mi/hr.

Downstream speed is:

6 miles

--------

2 hours

Dividing numerator and denominator by 2:

3 miles

--------

1 hour

That's 3 mi/hr.

Based on the information you provided.

Velocity = distance / time

Upstream

Velocity = 6 miles / 3 hours = 2 miles / hour

Downstream

Velocity = 6 miles / 2 hours = 3 miles / hour

Average velocity = 2.5 miles / hour

# Comments

Hi Neighbor!

let x be the speed of the current downstream.

let y be the speed of rowing.

3 (y - x) = 6 --------> (y - x) = 2 -------> y = x + 2 eq. 1

2( y + x) = 6 eq. 2

substitute eq. 1 to eq. 2:

2((x + 2) + x) = 6

2(2x + 2) = 6

2x + 2 = 3 --------------> 2x = 3 - 2 -------------> 2x = 1 ------> x = 1/2

substiture x into eq. 1:

y = 1/2 + 2 -------> y = 5/2

**upstream:**5/2 - 1/2 = 4/2 =

**2 miles/hour**

**downstream:**5/2 + 1/2 = 6/2 =

**3 miles/hour**

Hi Kelli;

upstream...6 miles, 3 hours, 2 mph

downstream...6 miles, 2 hours, 3 mph

downstream...(still-water-speed)+(current)=3 mph

upstream...(still-water-speed)-(current)=2 mph

Let's add the two equations together...

2(still-water-speed)=5 mph

**still-water-speed=2.5 mph**

Let's subtract the second equation from the first...

2(current)=1 mph

current=1/2 mph

Let's check our results...

upstream...

distance=(rate)(time)

6 m=[(2.5 mph)-(1/2 mph)][3 h]

6 m=(2 mph)(3 h)

The unit of hours is in the numerator and denominator of the right side of the equation. It cancels...

6 m=(2 m)(3)

6m=6m

downstream...

distance=(rate)(time)

6 m=[(2.5 mph)+(1/2 mph)][2 h]

6 m=(3 mph)(2 h)

6 m=(3 m)(2)

6=6

## Comments

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