Freshman math question, super confused!

Today while Don was swimming, he started
wondering how many lengths he would have to swim in order to swim different distances. At one end of the pool, he stopped, gasping for breath, and asked the lifeguard. She told him that 1 length of the pool is 25 yards and that 72 lengths is 1 mile. As he continued swimming, he wondered:

a. Is 72 lengths really a mile? Exactly how many lengths would it take to swim a mile?

b. If it took him a total of 40 minutes to swim a mile, what was his average speed in feet per second?

c. How many lengths would it take to swim a kilometer?

d. Last summer Don got to swim in a pool that was 25 meters long. How many lengths would it take to swim a kilometer there? How many for a mile?

a. well there are 1760 yards in a mile, so is 1760=25*72? No. 1760/25 = ?

b. 5280 ft / (40*60) s = 2.2 ft/s

c.1 km = 0.62 mile, so it would be 1760/25 * 0.62

d. 1km = 1000m, so it would be 1000/25 lengths. For a mile, it would be 1000/25 / 0.62

To answer these questions, we need to understand the relationships between the various measurements provided.

a. To determine if 72 lengths is really a mile, we need to convert yards to miles. We know that 1 length is 25 yards, and we need to find how many lengths make up 1 mile. Here's how you can calculate it:

1 mile = 1760 yards (since there are 1760 yards in a mile)
1 length = 25 yards

Number of lengths in 1 mile = (1760 yards) / (25 yards)
Number of lengths in 1 mile = 70.4 lengths

So, 1 mile is approximately equal to 70.4 lengths. Therefore, 72 lengths is more than a mile.

b. To find the average speed in feet per second, we need to convert the time taken to a unit of seconds. We are given that it took Don 40 minutes to swim a mile. Since there are 60 seconds in a minute, we can calculate the time taken in seconds:

40 minutes = 40 * 60 = 2400 seconds

We also know that 1 length is 25 yards. Since 1 yard is equal to 3 feet, we can calculate the distance in feet:

1 length = 25 yards = 25 * 3 feet = 75 feet

Therefore, Don swam a total of 75 feet * 72 lengths = 5400 feet.

Now, to find his average speed in feet per second, we divide the total distance by the time taken:

Average speed = 5400 feet / 2400 seconds
Average speed ≈ 2.25 feet per second

So, his average speed was approximately 2.25 feet per second.

c. To determine how many lengths it would take to swim a kilometer, we need to convert the distance from kilometers to yards, then divide by the length of 1 pool length. Here's how you can calculate it:

1 kilometer = 1000 meters
1 meter = 1.09361 yards

Number of yards in 1 kilometer = 1000 meters * 1.09361 yards/meter
Number of yards in 1 kilometer ≈ 1093.61 yards

Since 1 length is 25 yards, we can divide the total yards by the length of 1 pool length:

Number of lengths in 1 kilometer = 1093.61 yards / 25 yards
Number of lengths in 1 kilometer ≈ 43.74 lengths

Therefore, it would take approximately 43.74 lengths to swim a kilometer.

d. To find out how many lengths it would take to swim a kilometer and a mile in a 25-meter long pool, we will use the same methodology. Here's how you can calculate it:

1 kilometer = 1000 meters
1 meter = 3.28084 feet
1 meter = 1.09361 yards

Number of yards in 1 kilometer = 1000 meters * 1.09361 yards/meter
Number of yards in 1 kilometer ≈ 1093.61 yards

Since 1 length is 25 meters, the total yards can be converted to meters and then divided by the length of 1 pool length:

Number of lengths in 1 kilometer = (1093.61 yards / 1.09361 yards/meter) / 25 meters
Number of lengths in 1 kilometer ≈ 43.74 lengths

To determine the number of lengths it would take to swim a mile, we convert the 1760 yards to meters and divide by the length of 1 pool length:

Number of lengths in 1 mile = (1760 yards / 1.09361 yards/meter) / 25 meters
Number of lengths in 1 mile ≈ 69.04 lengths

Therefore, in a 25-meter long pool, it would take approximately 43.74 lengths to swim a kilometer and approximately 69.04 lengths to swim a mile.