SOLUTION: A motorboat traveling with the current went 35 mi in 3.5 h.Traveling against the current, the boat went 12 mi in 3h.Find the rate of the boat in calm water and the rate of the curr

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A motorboat traveling with the current went 35 mi in 3.5 h.Traveling against the current, the boat went 12 mi in 3h.Find the rate of the boat in calm water and the rate of the curr      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 815142: A motorboat traveling with the current went 35 mi in 3.5 h.Traveling against the current, the boat went 12 mi in 3h.Find the rate of the boat in calm water and the rate of the current.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Find boat speed & current speed Both times given

boat speed =x mph
current speed =y mph
against current 3 hours
with current 3.5 hours

Distance against 12 miles distance with 35 miles
t=d/r against current -
12.00 / ( x - y )= 3.00
3.00 ( x - y ) = 3.50
3.00 x - 3.00 y = 12.00 ....................1

35.00 / ( x + y )= 3.50
3.50 ( x + y ) = 35.00
3.50 x + 3.50 y = 35.00 ...............2
Multiply (1) by 3.50
Multiply (2) by 3.00
we get
10.50 x + -10.50 y = 42.00
10.50 x + 10.50 y = 105.00
21.00 x = 147.00
/ 21.00
x = 7.00 mph

plug value of x in (1) y
3.00 x -3.00 y = 12.00
21.00 -3.00 -21.00 = 12.00
-3.00 y = 12.00
-3.00 y = -9.00 mph
y = 3.00
boat speed 7.00 mph
current speed 3.00 mph