Question 1182755: Dan and Jane each have a measuring tape of length 1m. Dan's tape got stuck in a door and was extended by 4cm. Jane left her tape in a pocket and it shrank by 5 cm after washing. However, the centimetre marks on both tapes remained evenly distributed.
Measuring the schoolyard, Dan noted the length as 23.75m. What length will Jane get measuring the same schoolyard with her tape?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the length of the tape is 1 meter = 100 centimeters.
dan's tape measures 1 meter + 4 centimeters = 1.04 meters = 104 centimeters.
jane's tape measures 1 meter - 5 centimeters = .95 meters = 95 centimeters.
they both measured the length of the schoolyard with their tape measures.
the assumption that i think needs to be made is that they both still think their tape measures 1 meter = 100 centimeters.
in other words, they don't know that the length of their tapes has been distorted.
dan measures the length of the schoolyard as 23.75 meters = 2375 centimeters.
this means that he thinks that the length of his tape divides into 2375 by 2375 / 100 = 23.75 times.
since the length of this tape is actually 104 centimeters, then the length of the schoolyard is actually 23.75 * 104 = 2470 centimeters.
jane measures the length of the same schoolyard.
the actual length is 2470 centimeters.
her tape divides into 2470 centimeters 2470 / 95 = 26 times.
she thinks that her tape measures 100 centimeters, therefore she records the length of the schoolyard as 26 * 100 = 2600 meters.
given that the length of the schoolyard is actually 2470 centimeters, ...
he will measure 2470 / 104 * 100 = 2375 centimeters.
she will measure 2470 / 95 * 100 = 2600 centimeters.
i tried to confirm this is true by doing the following.
assume the actual length of the schoolyard is 1000 centimeters.
dan's tape will divide into this 1000 / 104 = 9.615384615 times.
since he thinks his tape measures 100 centimeters, he will report the length as 9.615384615 * 100 = 961.5384615 centimeters.
his measurement will be 961.5384615 / 1000 = .9615384615 times the actual measurement.
jane's tape will divide into this 1000 / 95 = 10.52631579 times.
since she thinks her tape measures 100 centimeters, she will report the length as 1052.631579 centimeters.
her measurement will be 1052.631579 / 1000 = 1.052631579 times the actual measurement.
take these ratios and apply to the problem at hand and you will get.
2375 / .9615384615 = 2470
2600 / 1.052631579 = 2470.
it appears that i did this right.
if so, then:
dan measures the schoolyard as 2375 centimeters = 23.75 meters.
jane measures the schoolyard as 2600 centimeters 26 meters.
the actual measurement of the schoolyard is 2470 centimeters = 24.70 meters.
your solution should be that jane measures the schoolyard as 26 meters.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
When Dan measures the length as 23.75m, the length he is actually measuring is 23.75 times 1.04m, which is 24.7m.
When Jane measures the length, each actual meter measures 0.95m, so the length in meters by her measuring tape is 24.7/0.95 = 26m.
ANSWER: Jane's measurement will be 26m.
Alternatively....
Jane's measuring tape is shorter than Dan's by a factor of 0.95/1.04. That means when measuring any object with the two tapes, Jane's measurement will be larger than Dan's by a factor of 1.04/.95.
ANSWER: Jane's measurement in meters will be 
|
|
|
