8. A mile-long train is moving at 60-miles-per-hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through?
9. How many 3-cent stamps are there in 4 dozen?
it takes the mile-long train 1 minute to pass any fixed point at 60 mph.
So, it takes 1 minute for the front of the train to pass through the tunnel.
At that point, the caboose is just entering the tunnel.
After one more minute, the caboose has exited the tunnel.
Total time: 2 minutes
To solve these questions, we need to apply some basic mathematical concepts.
8. To calculate the time it takes for the entire train to pass through the tunnel, we first need to determine the relative speed of the train compared to the tunnel. Since the train is moving at 60 miles per hour and the tunnel is also a mile long, we can consider the length of the train and the length of the tunnel together as a single entity with a length of 2 miles.
To calculate the time it takes to cover a distance, we use the formula: time = distance / speed. In this case, the total distance is 2 miles (train + tunnel) and the speed is 60 miles per hour. Therefore, the time it takes for the entire train to pass through the tunnel is 2 miles / 60 miles per hour = 1/30 hours.
Since we want to express the time in a more common unit, we can convert it to minutes. There are 60 minutes in an hour, so 1/30 hours is equal to (1/30) * 60 = 2 minutes.
Therefore, it takes the entire train 2 minutes to pass through the tunnel.
9. To find out how many 3-cent stamps are there in 4 dozen, we need to know the number of stamps in a dozen. A dozen refers to a group of 12 items. In this case, we have 4 dozen, so we have 4 groups of 12 items.
To calculate the total number of stamps, we multiply the number of groups (4 dozen) by the number of items per group (12). Therefore, the total number of stamps is 4 dozen * 12 = 48 stamps.
Since we want to find out the number of 3-cent stamps, we divide the total number of stamps (48) by the value of each stamp (3 cents). Therefore, the number of 3-cent stamps in 4 dozen is 48 stamps / 3 cents = 16 stamps.
Therefore, there are 16 3-cent stamps in 4 dozen.