Question 1182755
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.