SOLUTION: Bob paddled against current for 2 hrs. and then with current for 1 hr. and rested. Rick paddled against current for 2.5 hrs. and then with current for 1.5 hrs. If they paddled a

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Question 1031806: Bob paddled against current for 2 hrs. and then with current for 1 hr. and rested. Rick paddled against current for 2.5 hrs. and then with current for 1.5 hrs. If they paddled a total of 9.5 miles against the current and 20.5 miles with the current and the current is 3 mph. How fast do they paddle in still water?
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Bob paddled against current for 2 hrs. and then with current for 1 hr. and rested.
let Bob's speed in still water be x
with current his speed will be x+3 mph
with current he paddled for (x+3) * 1
against current his speed will be x-3 mph
against current he paddled f or (x-3)*2
Rick with current for 1.5 hrs.
let Rick's speed in still water be y
with current his speed will be y+3 mph
with current he paddled for (y+3) * 1.5

Rick paddled against current for 2.5 hrs.
against current his speed will be y-3 mph
against current he paddled f or (y-3)*2.5

If they paddled a total of 9.5 miles against the current
(x-3)*2 +(y-3)*2.5 = 9.5
2x-6 +2.5y -7.5 =9.5
2x+2.5y = 23...........................(1)
and 20.5 miles with the current
(x+3) * 1+ (y+3) * 1.5=20.5
x+3 +1.5y +4.5 =20.5
x+1.5y=13.......................(2)
2.00 x + 2.50 y = 23.00 .............1

1.00 x + 1.50 y = 13.00 .............2
Eliminate y
multiply (1)by -1.50
Multiply (2) by 2.50
-3.00 x -3.75 y = -34.50
2.50 x + 3.75 y = 32.50
Add the two equations
-0.50 x = -2.00
/ -0.50
x = 4.00
plug value of x in (1)
2.00 x + 2.50 y = 23.00
8.00 + 2.50 y = 23.00
2.50 y = 23.00 -8.00
2.50 y = 15.00
y = 6.00
x= 4.00 mph Bob's speed
y= 6.00 mph Rick's speed

m.ananth@hotmail.ca