Two cars, A and B, left AB at the same time. When they met, the distance they walked was 4: 3. After the meeting, B was faster than A by12km per hour, and A still walked at the original speed. As a result, the two cars arrived at the destination at the same time. It is known that B traveled 12 hours. How many kilometers is it between AB and China?

Solution: Let the speeds of Party A and Party B be 4a km/h and 3a km/h respectively.

therefore

4a× 12×(3/7)/(3a)+4a× 12×(4/7)/(4a+ 12)= 12

4/7+ 16a/7(4a+ 12)= 1

16a+48+ 16a=28a+84

4a=36

a=9

A =4×9=36 km/h speed.

AB distance = 36× 12 = 432km.

Arithmetic method:

Time after meeting = 12×3/7=36/7 hours.

Speed 12km, linear speed per second 12x36/7 = 432/7km.

When we met, A was more than B. 1/7.

Then the whole journey = (432/7)/( 1/7) = 432km.

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