SOLUTION: In his motorboat, Bill travels upstream at top speed to his favorite fishing spot, a distance of 36 miles. It takes him 2 hours. Returning, he finds that the trip downstream, still

Algebra ->  Systems-of-equations -> SOLUTION: In his motorboat, Bill travels upstream at top speed to his favorite fishing spot, a distance of 36 miles. It takes him 2 hours. Returning, he finds that the trip downstream, still      Log On


   

Question 715480: In his motorboat, Bill travels upstream at top speed to his favorite fishing spot, a distance of 36 miles. It takes him 2 hours. Returning, he finds that the trip downstream, still at top speed, only takes 1.5 hours. Find the speed of Bill's boat and the speed of the current.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Boat speed speed =x mph
current speed =y mph
against current 2 hours
with current 1.5 hours

Distance with current 36 miles distance against current 36
t=d/r against current (x-y)
36.00 / ( x - y )= 2.00

2.00 x - -2.00 y = 36.00 ....................1
with current (x+y)
36.00 / ( x + y )= 1.50
1.50 ( x + y ) = 36.00
1.50 x + 1.50 y = 36.00 ...............2
Multiply (1) by 1.50
Multiply (2) by 2.00
we get 2.00
3.00 x + -3.00 y = 54.00
3.00 x + 3.00 y = 72.00
6.00 x = 126.00
/ 6.00
x = 21 mph

plug value of x in (1) y
2 x -2 y = 36
42 -2 -42 = 36
-2 y = 36
-2 y = -6 mph
y = 3
Boat speed 21 mph
current 3 mph