Math Problem

Question

On a weekend outing? Charles rents a motorboat for 6 hours to travel down the river and back. The rental operator tells him to go for 2 hours downstream, leaving 4 hours to return upstream. If the river current flows at a speed of 6 mph, how fast must Charles travel in order to return in 6 hours?

Answer 1

distance=rate*time

d=r*t

d=(r+6)*2

d=(r-6)*4

equate the two right sides because they both equal d

(r+6)*2=(r-6)*4

divide both sides by 2

(r+6)=(r-6)*2

r+6=2r-12

6+12=2r-r

18=r

r=18 mph

Charles must travel at a speed of 18 mph

 

 

Answer 2

Hi Chelsea, these problems are application of the D(istance) = T(ime) * R(ate) equation. We can create two equations based on the downstream trip and the upstream trip.

 

One fact, which is not stated, but true is the distance traveled downstream must equal the distance traveled upstream.

 

Equation 1, trip downstream.

 

D = T * R

 

T = 2 hours

 

R = x (speed of the boat - unknown) + 6mph (speed of the river)

 

D = 2 * ( x + 6)

 

Equation 2, trip upstream.

 

D = T * R

T = 4 hours

R = x (speed of the boat - unknown) - 6mph (speed of the river)

D = 4 * ( x - 6)

 

Since the distance downstream must equal the distance upstream, we can write:

 

2 * (x + 6) = 4 * (x - 6)

 

2x + 12      = 4x - 24

 

Subtract 2x from both sides:

 

12 = 2x - 24

 

Add 24 to both sides:

 

36 = 2x

 

Divide both sides by 2:

 

x = 18, or the speed of the boat is 18mph.

 

Questions?