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?
To find the total number of wheels on the 60 vehicles, let's break down the given information step by step and count the wheels accordingly.
1. We know that every second vehicle was a taxi. This means half of the vehicles, i.e., 30 out of 60, were taxis. Taxis have 4 wheels each, so the total number of wheels from taxis is 30 * 4 = 120 wheels.
2. The odd prime numbered vehicles were human powered. So, let's identify these vehicles:
- The 3rd vehicle is counted as a bicycle.
- The 5th vehicle is counted as a bicycle.
- The 7th vehicle is counted as a bicycle.
- The 11th vehicle is counted as a bicycle.
- The 13th vehicle is counted as a bicycle.
- And so on...
It is important to note that the first two vehicles are not counted as bicycles because they are not odd prime numbers (2 and 3).
3. Three out of every four human-powered vehicles were bicycles. This means for every fourth human-powered vehicle, one will not be a bicycle. So, for our calculated list of human-powered vehicles, three out of four will have bicycles.
4. The odd multiples of 3 (excluding 3) were counted as mopeds. These vehicles will have 2 wheels each.
5. The remaining vehicles (that are not taxis, bicycles, or mopeds) are big trucks. We can calculate the number of big trucks by subtracting the number of taxis, bicycles, and mopeds from the total count of vehicles (60).
Now, let's calculate the number of wheels for each vehicle type:
- Taxis (4 wheels): 30 vehicles * 4 wheels = 120 wheels.
- Bicycles (2 wheels): Out of the prime numbered vehicles, every third one is a bicycle. So, we can count 6 bicycles from the given list.
- 6 bicycles * 2 wheels = 12 wheels.
- Mopeds (2 wheels): The odd multiples of 3 (excluding 3) will be mopeds. So, we can count the multiples: 6, 9, 15, 18, 21, 27, 33, 36, 39, 45, 48, 51, 57. That makes 13 mopeds.
- 13 mopeds * 2 wheels = 26 wheels.
- Big trucks (6 wheels): The remaining vehicles after counting taxis, bicycles, and mopeds are big trucks.
- 60 total vehicles - 30 taxis - 6 bicycles - 13 mopeds = 11 big trucks.
- 11 big trucks * 6 wheels = 66 wheels.
Finally, let's calculate the total number of wheels:
120 wheels (taxis) + 12 wheels (bicycles) + 26 wheels (mopeds) + 66 wheels (big trucks) = 224 wheels.
Therefore, on these 60 vehicles, there were a total of 224 wheels.