SOLUTION: Traveling against the current, the Scouts paddled 20km in 4 h. The return trip with the current took 1.5 h less. Find (a) the Scout's paddling rate in still water and (b) the rate

Question 121239: Traveling against the current, the Scouts paddled 20km in 4 h. The return trip with the current took 1.5 h less. Find (a) the Scout's paddling rate in still water and (b) the rate of the current.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Traveling against the current, the Scouts paddled 20 km in 4 h. The return trip with the current took 1.5 h less. Find (a) the Scout's paddling rate in still water and (b) the rate of the current.
;
Let x = paddling rate in still water
Let y = rate of the current:
:
Time upstream given as 4 hr
Time downstream: 4 - 1.5 = 2.5 hrs
:
Write two distance equations:
one for upstream and one for downstream (Dist = time * speed
4(x-y) = 20
2.5(x+y) = 20
:
Simplify both equations: divide the 1st eq by 4 and the 2nd eq by 2.5
x - y = 5
x + y = 8
------------adding eliminates y, find x
2x + 0 = 13
x = 13/2
x = 6.5 km/h speed in still water
:
Find y using x + y = 8
6.5 + y = 8
y = 8 - 6.5
y = 1.5 km/hr is the current
:
Check solution by finding if the distances are equal
4(6.5 - 1.5) = 20
and
2.5(6.5 + 1.5) = 20
;
Could you follow this OK?
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