SOLUTION: A speedboat could travel at 6 times the speed of the current. Thus, it could travel 350 miles downriver in 3 hours more than it took to travel 150 miles upriver. What was the sp

Question 142725: A speedboat could travel at 6 times the speed of the current. Thus, it could travel 350 miles downriver in 3 hours more than it took to travel 150 miles upriver. What was the speed of the boast in still water?
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 r=rate of the current
Then 6r=rate of speedboat in still water
Rate upriver =6r-r=5r
Rate downriver=6r+r=7r
Time to travel up river=150/5r
Time to travel down river =350/7r
Now we are told the following:
(150/5r)+3=350/7r simplify
(30/r)+3=50/r multiply each term by r
30+3r=50 subtract 30 from each side
30-30+3r=50-30
3r=20 divide each side by 3
r=6 2/3 mph-------------------speed of current
6r=6*(6 2/3)=40 mph--------------------------speed (rate) of boat in still water

CK
(150/(5*6 2/3))+3=350/(7*6 2/3)) and this equals
30/(20/3)+3=50/(20/3)
90/20 +3 =150/20
4.5+3=7.5
7.5=7.5

Hope this helps---ptaylor

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