SOLUTION: if a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still wtaer respectively are ?

Question 199864: if a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still wtaer respectively are ?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
if a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours,
the rate of the river and the rate of the boat in still water respectively are ?
:
Let x = boat speed in still water
Let y = rate of the current
then
(x+y) = speed down stream
(x-y) = speed up stream
:
Write a distance equation for each trip: time * speed = dist
:
3(x+y) = 72
6(x-y) = 60
:
Simplify both equations;
divide the 1st equation by 3,
divide the 2nd equation by 6
results:
x + y = 24
x - y = 10
---------------addition eliminates y, find x
2x = 34
x =
x = 17 mph in still water
:
Find y using equation: x + y = 24, substitute 17 for x
17 + y = 24
y = 24 - 17
y = 7 mph is the current
;
:
Check solution in the 2nd original equation: 6(x-y) = 60
6(17 - 7) = 60
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