I measured the distance between two points by the tape measure of the A and B with the scale of 50 m.
As a result of having measured by A, it was 833 m having measured by B, it was 835 m.
When there was the deviation in these two tape measures and compared length of A and B, there was a difference of 12 cm by a right measure.
Answer the following questions.
(1) How much is the deviation of A and B with a right measure each ?
(2) It is 1000 m of the distance measured in a tape measure of A and how long is the distance in case measured in a right measure ?
(3) How long is the correct distance between two points ?
As a result of having measured by A, it was 833 m having measured by B, it was 835 m.
When there was the deviation in these two tape measures and compared length of A and B, there was a difference of 12 cm by a right measure.
Answer the following questions.
(1) How much is the deviation of A and B with a right measure each ?
(2) It is 1000 m of the distance measured in a tape measure of A and how long is the distance in case measured in a right measure ?
(3) How long is the correct distance between two points ?
Answer
835 - 833 = 2 and 2 is differences between A and B is equivalent to 12 cm with a right measure. 1 = 12 cm / 2 = 6 cm.
Then the length of A is 835 = 6 cm × 835 =5010 cm and the length of B is 833 = 6cm × 833 = 4998 m.
Therefore the deviation of A is 10 cm and B is 2 cm.
(2) As the ratio of the length of A and the right measure is 5010 : 5000, the ratio of the distance measured becomes 5000 : 5010 in inverse proportion.
Therefore, the distance of 1000 m measured by A is 1000 × 5010/5000 =1002 m by a right measure.
(3) As the ratio of the distance measured becomes
The correct distance by the right measure is 833 × 5010/5000 = 834.666 m.
(1) A : 10 cm, B : 2 cm
(2) 1002 m
(3) 834.666 m
(2) 1002 m
(3) 834.666 m
Solution
(1) When I measure the same distance with two tape measures with some deviation, the ratio of the right length of two measures becomes the inverse proportion of the ratio of distance measured in each tape measure.
As the ratio of the distance is 833 m by A : 835 m by B, the ratio of the length of A and B is 835 : 833.
As the ratio of the distance is 833 m by A : 835 m by B, the ratio of the length of A and B is 835 : 833.
835 - 833 = 2 and 2 is differences between A and B is equivalent to 12 cm with a right measure. 1 = 12 cm / 2 = 6 cm.
Then the length of A is 835 = 6 cm × 835 =5010 cm and the length of B is 833 = 6cm × 833 = 4998 m.
Therefore the deviation of A is 10 cm and B is 2 cm.
(2) As the ratio of the length of A and the right measure is 5010 : 5000, the ratio of the distance measured becomes 5000 : 5010 in inverse proportion.
Therefore, the distance of 1000 m measured by A is 1000 × 5010/5000 =1002 m by a right measure.
(3) As the ratio of the distance measured becomes
5000 : 5010 = 833: (the length measured by the right measure).
The correct distance by the right measure is 833 × 5010/5000 = 834.666 m.
