Rowing Upstream and DownDate: 5/9/96 at 0:38:9 From: Beverly Kay Cash Subject: Distance problems Here is the problem. Karen can row a boat 10 kilometers per hour in still water. In a river where the current is 5 kilometers per hour, it takes her 4 hours longer to row x kilometers upstream than the same distance downstream. Find x. Here is what I have so far. d r t downstream x 10kph x _________ 10 kph upstream x 10k/4hrs x .25kph ________ .25kph What do I do with the 5kph and how do I set it up to solve it? Date: 10/17/96 at 8:20:21 From: Doctor Jerry Subject: Re: Distance problems Dear Beverly, I think we must assume that the x kilometers upstream is measured relative to the bank. So, we must calculate rates relative to the bank. When Karen is rowing upstream, her rate is 10 - 5 = 5, relative to the bank. Your analysis above, in the table, is well laid out, but the values under r don't take into account the "relative to the bank" idea. What is her rate downstream? If you recalculate the rates, you will have used the 5kph. If you let Tu be the time upstream and Td the time downstream, then, since the distances are the same, you can equate Ru*Tu and Rd*Td. This gives a relation between Tu and Td. Finally, you know something about the difference of the times. This will give an equation. One final thought. If you are on a bus, which is zooming down the highway at 100kph, and walk at 5kph towards the front of the bus, you are moving at 105kph relative to the highway. Right? I hope this answers your questions. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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