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# 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?

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?

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.

so clear, thanks?
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

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