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?

Question

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

Answer 1

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.

Answer 2

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

Answer 3

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

 

 

Answer 4

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