math
posted by mindy on .
A boat traveled 45 miles downstream (w/ the current) in 3 hours and made the return trop (against the current) in 5 hours. What was the speed of the boat and what was the speed of the current?

b=boat (mph)
c=current (mph)
Set up equations using distance=speed*time
3(b+c)=45 ...(1)
5(bc)=45 ...(2)
Multiply (1) by 5 and (2) by 3:
15b+15c = 225 ...(1a)
15b15c = 135 ...(2a)
Add (1a) and (2a)
30b+0 = 360
b = 360/30 = 12
Subtract (2a) from (1a)
0+30c = 90
c = 90/30 = 3
Boat speed is 12 mph,
current speed is 3 mph 
speed of boat  x mph
speed of current  y mph
then :
1. 3(x+y) = 45 or x+y = 15
2. 5(xy) = 45 or xy = 9
add them:
2x = 24
x = 12
from one of the others, y = 3
etc. 
thank you guys so much