Rate/time/distance problem

Question

A boat takes 3 hrs to go 24 mi upstream against the current. It can go downstream with the current a distance of 48 mi in the same amount of time. Determine the speed of the boat in still water and the speed of the current.

Answer 1

Up:

24 = (r - c)3

Down:

48 = (r + c)3

 

24 = 3r - 3c

48 = 3r + 3c

 

 

Can you solve the system?

Answer 2

Distance = rate * time ...    d = rt

 

Let b = speed of boat in still water

Let c = current speed

------------------------------------------------

Speed upstream is boat speed minus current speed

r = b-c

 

Upstream:  24 = 3(b-c)

---------------------------------------------

Downstream rate is boat speed plus current speed

r = b+c

 

downstream:  48 = 3(b+c)

----------------------------------

 

We have two equations with two unknowns

 

3b-3c = 24         upstream

3b+3c = 48        downstream

--------------       add the equations and solve for b

6b       = 72    

 

b = 12 mph

 

plug that into one of the equations and solve for c

 

3b+3c = 48

3(12)+3c=48

36+3c = 48

3c = 12

c = 4 mph

 

The boat speed is 12 mph in still water

the current speed is 4 mph