Max swims the breaststroke for 4 laps at the speed of 50 meters per minute. He then switches to the backstroke and swims another 4 laps at the speed of 25 meters per minute. A If length of the pool is d meters, how long did it take Max to complete 4 laps breaststroke?

Max swims the breaststroke for 4 laps at the speed of 50 meters per minute. He then switches to the backstroke and swims another 4 laps at the speed of 25 meters per minute.

a) If length of the pool is d meters, how long did it take Max to complete 4 laps breaststroke?

b) How long did it take Max to complete 4 laps backstroke?

c) It took him 2 minutes longer to complete 4 laps backstroke than 4 laps breaststroke. Write the equation that describes this fact.

d) What is the length of the swimming pool?

Solution:

a) Speed is the ratio of distance to time, it is given as:

speed = distance/time

1 lap = d meters, hence:

4 laps = 4d meters

Max swims the breaststroke at 50 meters per minute. Let us assume the time taken to complete 4 laps is [tex]t_1[/tex] minutes hence:

50 = 4d/[tex]t_1[/tex]

[tex]t_1\\[/tex] = 4d/50

[tex]t_1[/tex] = 2d/25 minutes

b) 1 lap = d meters, hence:

4 laps = 4d meters

Max swims the backstroke at 25 meters per minute. Let us assume the time taken to complete 4 laps is [tex]t_2[/tex] minutes hence:

25 = 4d/[tex]t_2[/tex]

[tex]t_2[/tex] = 4d/25 minutes

c) Since It took him 2 minutes longer to complete 4 laps backstroke than 4 laps breaststroke

[tex]t_2=t_1+2[/tex]

c)

[tex]t_2=t_1+2[/tex]

[tex]\frac{4d}{25}= \frac{2d}{25}+2\\\\multiply\ through\ by\ 25:\\\\4d = 2d +50\\\\4d-2d=50\\\\2d=50\\\\d=25\ meters[/tex]

The pool is 25 meters long