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

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

RELATED QUESTIONS
Steve�s canoe goes 14km/hr in still water. He paddled for 2 hours with the current to... (answered by josmiceli)

Paddling for 4 hrs with a 6 km/hr current and a return trip against the same current took (answered by ankor@dixie-net.com)

a canoeist paddled for 4 hrs with a 6km/h current to reach a campsite.the return trip... (answered by checkley71)

Alvin paddled for 2 hours with a 6-km/h current to reach a campsite. The return trip... (answered by richard1234)

Fred paddled for 3 hours with a 5 km/hr current to reach a campsite. The return trip... (answered by checkley77)

alvin paddled for 2 hours with a 5-km/h current to reach a campsite. the return trip... (answered by jorel1380)

Alvin paddled for 5 hours with a 2-km/h current to reach a campsite. The return trip... (answered by mananth)

Dan and cheryl paddled their canoe 40 mi in 5 hr with the current and 16 mi in 8 hr... (answered by josgarithmetic)

Fred paddled for 5 hours with 7km/hr current to reach a campsite. The return trip against (answered by Alan3354)