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Subject: RATE OF BOAT AND RIVER My Son and I are having a hard time with this question: If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hour, the rate of the river and the rate of the boat in still water respectively are ____? Thank you for your help.
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Hi Dale. Let's call the rate of the current with respect to the land C miles per hour and the rate of the boat with respect to still water B miles per hour. Remember that distance = speed times time. Going downstream 72 miles for 3 hours, the current and the boat are working together, so the total speed is B+C. This means that 72 = (B+C) x 3. Coming back upstream for 60 miles in 6 hours, the current works against the boat, so the total speed is B-C. This means that 60 = (B-C) x 6. Now take both of these equations and turn them into equations that "solve for B":
and
Now we have two different expressions with C that both equal B. Since two things that equal a third thing must be equal to each other, that means
From here, I am sure you can solve for C (the current speed) and then use this value in either one of the original equations to find B, the boat speed in still water. Hope this helps, |
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