Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem30

Video Transcription

Question number 30. Yuriko saw a tractor slowly pulling a long pipe down the road. Yuriko walked along beside the pipe in the same direction as the tractor and  counted 140 paces to get from one end to the other. He then turned around and walked back to the other end taking only 20 paces. The tractor and Yuriko kept a  uniform speed and Yuriko's paces were all one meter long. The question is how long was the pipe? So before we start comparing distances and times let's  write down some variables. Let's say P is the length of the pipe and Yuriko's speed would be Y  and capital T would be the tractor speed.  And then what we notice is that while Yuriko took 140 paces in one direction, so that's 140 meters at his speed, the tractor moved a total of 140 meters  minus whatever the length of the pipe was at the tractor speed. So we have one equation and now going back Yuriko paced 20 paces so 20 meters at his  speed and that time was equal to the time the tractor moved the length of the pipe minus whatever Yuriko walked because he's walking now in the opposite  direction over the tractor's speed. And so with these two relationships we can solve for the length of the pipe. So we will divide those equations. We have 140  divided by Y over 20 divided by Y. Let me just suppress the units for now and that's equal to 140 minus P divided by T all over P minus 20 divided by T. And so  that's the same equation as on the left-hand side we have 140 divided by 20 so let's just say that's 7 right away and equal to 140 minus P divided by P  minus 20. And then we can keep going with our calculation multiply both sides by P minus 20 so we have 7 P minus 140 is equal to 140 minus P or finally 8 times  the length of the pipe is equal to 280 and so the length of the pipe is 35 and that's in meters.

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