SOLUTION: a steamboat travels 12mi downstream in only 2h. the return trip upstream takes 3h. find the speed of the sailboat in still water and rate of the current
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Question 841621: a steamboat travels 12mi downstream in only 2h. the return trip upstream takes 3h. find the speed of the sailboat in still water and rate of the current
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
let x=rate of the steamboat in still water and y=rate of current
Downstream: d=rt
speed downstream=speed in still water + speed of current, sooo:
12=(x+y)*2 or 2x+2y=12----eq1
Upstream d=rt
speed upstream =speed in still water - speed of current:
12=(x-y)*3 or 3x-3y=12----eq2
multiply eq1 by 3 and eq2 by 2 then add the two equations:
6x+6y=36
6x-6y=24
--------
12x=60
x=5 mph----speed of the steamboat in still water
substitute x=5 into eq1:
2*5+2y=12
2y=2
y= 1 mph speed of the current
CK
downstream
12=6*2
12=12
upstream
12=4*3
12=12
Hope this helps---ptaylor
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