Question 871365: A boat travels downstream 10 miles in 2.5 hrs. The return trip takes 45 minutes. What's the speed of the boat and river? Answer by mananth(16946) (Show Source):
Distance against 10 miles distance with 10 miles
t=d/r against current -
10.00 / ( x - y )= 2.50
2.50 ( x - y ) = 0.75
2.50 x - 2.50 y = 10.00 ....................1
10.00 / ( x + y )= 0.75
0.75 ( x + y ) = 10.00
0.75 x + 0.75 y = 10.00 ...............2
Multiply (1) by 0.75
Multiply (2) by 2.50
we get
1.88 x + -1.88 y = 7.50
1.88 x + 1.88 y = 25.00
3.75 x = 32.50
/ 3.75
x = 8.67 mph
plug value of x in (1) y
2.50 x -2.50 y = 10.00
21.67 -2.50 -21.67 = 10.00
-2.50 y = 10.00
-2.50 y = -11.67 mph
y = 4.67
boat speed 8.67 mph
current speed 4.67 mph
