Devin is training for a competitive race by swimming and running. He covers a total distance of 9 km by swimming for 45 minutes and running for 20 minutes. The following day he swims for 30 minutes and runs for 40 minutes, covering a total of 14 km. Which system of linear equations can be used to find Devin's swimming rate (x) and his running rate (y) in kilometers per hour? A) 3 4 x + 1 3 r = 9 1 2 x + 2 3 y = 14 B) 3 4 x + 1 3 y = 14 1 2 x + 2 3 y = 9 C) 3 4 x + 1 3 y = 9 1 2 x - 2 3 y = 14 D) 3 4 x + 1 3 y = 23 1 2 x + 2 3 y = 23

The system is:

(3/4) x + (1/3) y = 9 (1/2) x + (2/3) y = 14

Explanation:

You must translate the two verbal statements into algebraic expressions, under the assumption that the swimming rate and the running rate are constant.

The names of the variables are given:

Swimming rate in kilometers per hour: x Running rate in kilometers per hour: y

1. First verbal statement

He covers a total distance of 9 km by swimming for 45 minutes and running for 20 minutes.

The distance covered is equal to the rate multiplied by the time.

distance = rate * time

Since the rates are in km/h, you mus change the times from minutes to hours:

Swimming time = 45min = (45/60) hours = (3/4) hour Running time = 20 min = (20/60) hours = (1/3) hour

Swimming distance = (3/4) x Running distance = (1/3) y

Total distance = 9km

9 = (3/4) x + (1/3) y ← first equation

2. Second verbal statement

The following day he swims for 30 minutes and runs for 40 minutes, covering a total of 14 km.

Swimming time = 30 min = (1/2) hour Running time = 40 min = (40/60) hours = (2/3) hour

Swimming distance = (1/2) x Running distance = (2/3) y

Total distance = 14km

14 = (1/2) x + (2/3) y ← second equation

Hence, the system is:

(3/4) x + (1/3) y = 9 (1/2) x + (2/3) y = 14