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Maybe if you stopped cheating on your AoPS homework and were actually interested in learning you wouldn't have to ask three times for your goddam bloody question to be answered.

GA

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In 4 hours at 60 miles per hour, he travels 4 hours * 60 miles per hour = 240 miles. In 8 hours at 45 miles per hour, he travels 8 hours * 45 miles per hour = 360 miles. In total, he travels 240 miles + 360 miles = 600 miles. In total, he drives for 4 hours + 8 hours = 12 hours. Therefore, his average speed is 600 miles / 12 hours = 50 miles per hour. So the answer is 50

After 15 minutes the worm will be 15*60*3=2700 cm out of point A. 8-3=5 cm the ant is gaining on the worm each second. 2700/300=9 minutes.

The problem shows that since the masons work at the same rate each Mason covers a third of the front of the house in four days. This means that it does 1/12 of the front in one day. Using this, we see that 16 brick masons will finish one and one third of a house in a day. 60/(4/3) = 45 days.

Mark drives 240+360=600 miles for the whole trip. It took him 12 hours in total and that gives an average of 600/12= 50 mph for the trip.

Please do not post AoPS Beast Academy questions.

a)  each of the other 6 rows has 8 less 

          73 - 6 *8 = 25 in the top row

b)       \(\sum_{0}^{6}\)  73 - 8n  = 343 boxes    

The lowest prime in the list would be 11     400/11 = 36.4    so the biggest prime int the list will be 31    11*31 = 341

   so from 11 to 31   the list of primes is  11  13  17  19   23  29  31    

           11 x the other 6   is 6 possibilities 

               13 x  17, 19,23,29    is 4 more possibles

                      17 x 19,  23   is two more 

                          and that is all          12 possible products 

A chain with two links is 13 cm long. A chain made from three links of the same type is 28 cm long. How many centimeters are in the length of a chain made from 25 such links?    

Let's take a run at this improbable-looking problem.  

Start with a 2 links chain, which is 13 cm long.   

Add one link, you get a 3 links chain, 28 cm long.    

We note that adding one link adds 15 cm to the length. 

Therefore, adding 23 links should add 23 x 15 = 345 cm to the length.  

The original 2 links, which is 13 cm long  

plus another 23 links, which is 345 cm long   

gives us a 25 links chain, which is 358 cm long.  

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