Mathes problems

~~Aurora Fantasia~~

2008-08-04 1:01 am

1.A mouse at point A runs due east along one side of the rectangle. At the
same time, a cat at point A runs due south along another side of the rectangle. Finally, they meet at point C, where BC=60cm. Given that the speed of the
mouse is 11/14 times of that of the cat, find the perimeter of the rectangle in metre.

Please help me to solve the problem!
Please remember to show the process of the operation.

回答 (1)

用戶5209

2008-08-04 1:02 am

✔ 最佳答案

Answer: the perimeter of the rectangle is 10 metres.

Solution:

let the perimeter of the rectangle be y metre

at point C,

the mouse runs ( y / 2 ) - 0.6 metre

the cat runs ( y / 2 ) + 0.6 metre

let the speed of the cat be v m/s

thus, the speed of the mouse is ( 11v / 14 ) m/s

since the time that the mouse need to run to point C

= the time that the cat need to run to point C,

[( y / 2 ) - 0.6 ] / ( 11v / 14 ) = [( y / 2 ) + 0.6 ] / v

( y / 2 ) - 0.6 = [( y / 2 ) + 0.6 ] ( 11v / 14 ) / v

( y / 2 ) - 0.6 = [( y / 2 ) + 0.6 ] ( 11 / 14 )

14[( y / 2 ) - 0.6 ] = 11[( y / 2 ) + 0.6 ]

7y - 8.4 = 5.5y + 6.6

7y - 5.5y = 6.6 + 8.4

1.5y = 15

y = 10

therefore, the perimeter of the rectangle is 10 metres

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