2016 APE Tutoring Junior High School Math contest training Camp homework answer-13

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1. A ship from Chongqing to Shanghai to $5$ Day and night, from Shanghai to Chongqing to $7$ Day and night, then there is a raft from Chongqing to Shanghai to how many days and nights?

Answer:

Set the flow velocity to $x $, then $ $x = \left (\frac{1}{5}-\frac{1}{7}\right) \div 2 = \frac{1}{35}.$$ therefore need $35$ day and night.

2. Between 10 o'clock and 11 o'clock, what is the time of two stitches in a straight line?

Answer:

$\delta S = 300-180 = 120$, $\delta V = 6-\dfrac{1}{2} = \dfrac{11}{2}$, $$\rightarrow T = \frac{\delta S}{\Delta V} = \frac{240}{11}.$$ so at $10$ Point $21\dfrac{9}{11}$ tick, two stitches into a straight line.

3. Silver and copper alloy $200$ G, which contains silver $2$ parts, containing copper $3$ parts, now to change the composition of the alloy, so that it becomes a silver containing $3$, containing copper $7$ parts, should be added to copper how much?

Answer:

Should be added copper $x $ g. $$ (+ x) \cdot \frac{7}{10} = \times \frac{3}{5} + x$$ $$\rightarrow x = \frac{200}{3}.$$ so should be added copper $\d frac{200}{3}$ G.

4. Hard aluminum is $4\%$ copper, $1\%$ manganese, $0.5\%$ magnesium and $94.5\%$ aluminum preparation, melting loss rate according to $1.5\%$ calculation. Manufacturing $250$ kg hard aluminum, how many kilograms of the above materials? (Keep one decimal place)

Answer:

The total amount of raw materials required for the establishment is $x $. $$\rightarrow X\cdot (1-1.5\%) = \rightarrow x = \frac{25000}{98.5},$$ therefore requires copper $$\frac{25000}{98.5} \times \frac{4}{10 0} \approx 10.2,$$ need manganese $$\frac{25000}{98.5} \times \frac{1}{100} \approx 2.5,$$ need mg $$\frac{25000}{98.5} \times \frac{0.5} {\approx 1.3,$$ need aluminum $$\frac{25000}{98.5} \times \frac{94.5}{100} \approx 239.8.$$

2016 APE Tutoring Junior High School Math contest training Camp homework answer-13