I was watching the street, there were mopeds(2 wheels) bikes(2 wheels), tricycles(3 wheels), taxis(4 wheels) and big trucks(6 wheels). I counted as they went past a total of 60 in 5 minutes. I notice the following about the vehicle. Every second was a taxi. Every odd prime numbered vehicle was human powered.so the 3rd, 5th, and 7th,11th, 13th and so on, three out of every four human powered vehicles were a bicycle. The odd multiples of 3(not included 3) were mopeds.and the remaining was big trucks. How many wheels went by on these 60 vehicles?
taxi: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 ...
bike/trike: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
moped: 9 15 21 27 33 39 45 51 57
truck: 1 25 35 55 49
30 taxis
9 mopeds
5 trucks
so, 16 humans: 12 bikes, 4 trikes
total wheels:
4*30 + 9*2 + 5*6 + 12*2 + 4*3 = 204
To find out how many wheels went by on these 60 vehicles, we need to analyze the given information step by step.
First, let's find out the proportion of each type of vehicle in the total count.
We know that every second vehicle is a taxi, so let's calculate how many taxis were in the 60-vehicle count. Since there are 60 vehicles in total, and every second vehicle is a taxi, we can divide 60 by 2:
60 / 2 = 30 taxis.
Next, according to the given information, every odd prime numbered vehicle is human-powered. To find the number of human-powered vehicles, we need to identify the odd prime numbers within the range of 1 to 60. The odd prime numbers in this range are 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, and 59. There are 16 odd prime numbers among the 60 vehicles.
Now, let's determine the number of bicycles and mopeds among the human-powered vehicles. According to the provided information, three out of every four human-powered vehicles are bicycles. So, we can calculate this as follows:
Number of bicycles = (3/4) * Total number of human-powered vehicles
= (3/4) * 16
= 12 bicycles.
To find the number of mopeds, we take the odd multiples of 3 (not including 3) among the human-powered vehicles. The odd multiples of 3 in this range are 9, 15, 21, 27, 33, 39, and 51. Hence, the number of mopeds is 7.
Finally, we can calculate the number of big trucks by subtracting the number of taxis, bicycles, and mopeds from the total count:
Number of big trucks = Total count - Number of taxis - Number of bicycles - Number of mopeds
= 60 - 30 - 12 - 7
= 11 big trucks.
Now, let's calculate the total number of wheels by multiplying the count of each type of vehicle by the number of wheels it has and summing them up:
Number of wheels = (Number of taxis * 4) + (Number of bicycles * 2) + (Number of tricycles * 3) + (Number of big trucks * 6)
= (30 * 4) + (12 * 2) + (16 * 3) + (11 * 6)
= 120 + 24 + 48 + 66
= 258 wheels.
Therefore, on these 60 vehicles, a total of 258 wheels went by.