HELP!!! Super confused. Here's the problem.

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?

72 lengths of 25 yards = 1800 yards

1 mile = 1760 yards, so he swam farther than a mile

to swim a mile:
1760/25 = 70.4
So he would need about 70 1/2 length to swim a mile, (might as well finish the 71 st length)

b)
1 mile = 5280 ft
rate = 5280/(2400) ft/sec = 11/5 or 2.2 ft/sec

c) 1 km = appr 1093.6 yds
number of length fo r 1 km = 1093.6/25 = 43.7 lengths

d) number of lengths to swim 1 km in a 25 m pool
= 1000/25 = 40

to swim 1 mile in a 25 m pool (there are 1609.344 m in 1 mile)
= 1609.344 /25 = 64.37 lengths

(time to get rid of all that mile, yards, feet etc, and go metric)

a. To determine exactly how many lengths it would take to swim a mile, we need to know the length of a mile in yards. We are given that 72 lengths of the pool is equivalent to 1 mile, but we want to find the number of lengths needed for exactly 1 mile.

To solve this, we can set up a proportion using the given information:
Length of 72 lengths (in yards) / 72 lengths = Length of 1 mile (in yards) / x lengths

Since we know that 1 mile is 1760 yards, we can substitute this value into the proportion:
(Length of 72 lengths) / 72 = 1760 / x

To find x, we can cross-multiply and solve for x:
Length of 72 lengths * x = 72 * 1760
x = (72 * 1760) / (Length of 72 lengths)

b. To find Don's average speed in feet per second, we need to convert the time he took to swim a mile from minutes to seconds. We are given that it took him 40 minutes to swim a mile.

Since there are 60 seconds in a minute, we can convert 40 minutes to seconds by multiplying by 60:
40 minutes * 60 seconds/minute = 2400 seconds

Now, we can calculate the average speed using the formula:
Speed = Distance / Time

Given that the distance is 1 mile (1760 yards) and the time is 2400 seconds, we can substitute these values into the formula:
Speed = 1760 yards / 2400 seconds

To find the average speed in feet per second, we also need to convert the distance from yards to feet. Since there are 3 feet in a yard, we can multiply the distance (in yards) by 3:
Speed = 1760 yards * 3 feet/yard / 2400 seconds

c. To determine how many lengths it would take to swim a kilometer, we need to know the length of a kilometer in yards. Since we are not given the exact conversion factor, we will need to look it up. One kilometer is approximately equal to 1093.61 yards.

Using the same proportion method as in part a, we can set up the equation:
(Length of 72 lengths) / 72 = 1093.61 / x

Cross-multiplying and solving for x:
Length of 72 lengths * x = 72 * 1093.61
x = (72 * 1093.61) / (Length of 72 lengths)

d. To determine how many lengths it would take to swim a kilometer in a pool that is 25 meters long, we need to convert the length of the pool to yards. Since there are 0.9144 yards in a meter, we can calculate the length of the pool in yards:
Length of pool in yards = 25 meters * 0.9144 yards/meter

To determine the number of lengths needed to swim a kilometer, we can set up a proportion using the length of the pool in yards and the conversion factor for 1 kilometer to yards (which is approximately 1093.61):
(Length of pool in yards) / x = 1093.61 / 1

Solving for x:
Length of pool in yards = x * 1093.61
x = Length of pool in yards / 1093.61

Finally, to find the number of lengths needed to swim a mile, we can use the same method as in part a, but with the given conversion factor of 72 lengths = 1 mile.