6 word problem

Question

It takes a boat 3 hours to travel 51 miles downstream and 4 hours to travel 44 miles upstream.

What is the speed of the boat in still water?
The boat travels at_____miles per hour in still water.

What is the speed of the current of the river?
The speed of the current is _____miles per hour.

Answer 1

Distance = Rate*Time   ...  d=rt

 

Let b = boat speed in still water

Let c = current speed

rate downstream = boat speed plus current speed

rate upstream = boat speed minus current speed

 

downstream:  51 = 3(b+c)

upstream:      44 = 4(b-c)

 

We have two simultaneous equations to solve:

 

1.   3b+3c = 51

2.   4b-4c = 44

 

multiply equation 1 by 4 and equation 2 by 3 and add

to eliminate the variable c

 

1.  12b + 12c = 204

2.  12b - 12c = 132

  ------------------------

     24b = 336

     b = 336/24

     b = 14 mph

 

Plug 14 in for b in either original equation and solve for c

 

3b+3c=51

3(14)+3c=51

42 + 3c = 51

3c = 9

c = 3 mph