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The first grade mathematics synchronization volume one answer.
1, allocation problem

Equal relationship: two people finally get the same amount of sugar.

That is: the amount of sugar that Xiao Ming gets = the amount of sugar that Xiao Ying gets.

Suppose there is a candy X.

Then Xiaoming's candy is: 1+(X- 1)/7.

(At this time, there are X- 1-(X- 1)/7 candies left. )

Xiaoying gets 2+[x-1-(x-1)/7-2]/7.

So1+(x-1)/7 = 2+[x-1-(x-1)/7-2]/7.

The solution is x = 36.

A: The original 36 pieces of sugar.

2. The key formula of travel problem is: speed * time = distance.

Equivalence: The speed of crossing two tunnels is the same.

Let the conductor be x meters (total length when passing through the tunnel = tunnel length+conductor)

Speed of the first tunnel = (256+x)/36

Second tunnel speed = (96+x)/ 16.

So (256+x)/36 = (96+x)/ 16.

The solution is x = 32.

This train is 32 meters long.