Lucia ran the 400-meter race 3 times. Her fastest time was 52.2 seconds. Her slowest time was 56.3 seconds. If Luzia's average time was 54.0 seconds, what was time for the third race?

53.5 sec

Step-by-step explanation:

Given

Number of times Lucia ran the race=n=3

Slowest time = x_1=56.3 sec

Fastest Time = x_2=52.2 sec

Average time=54.0 sec

Since, we know the average time and two of the three race times, we can use the average formula to calculate the third race's time.

Let

x_3=the third race^' s time

So,

Average = (Sum of values) / (Number of values)

Average = (x_1 + x_2 + x_3) / n

Putting the values

54.0 = (56.3 + 52.2 + x_3) / 3

Multiplying 3 with 54.0 and adding 56.3 and 52.2

162 = 56.3+52.2 + x_3

162 = 108.5 + x_3

x_ (3) = 162-108.5

x_ (3) = 53.5 sec

...