Question

The 4 members of the 1600m relay team run the 400m in an average time of 49.2 seconds. The fastest and slowest runner's times vary by 1.8 seconds from the team average. The equation that could be used to find the fastest and slowest times is

∣t−48.2∣=1.8. Solve the equation and fill in the blanks below:

a. Fastest runner's time: 50 seconds
b. Fastest runner's time: 48.2 seconds
c. Slowest runner's time: 49.2 seconds
d. Slowest runner's time: 46.2 seconds

Answer 1

The correct answer is option d. Slowest runner's time: 46.2 seconds. To solve the equation ∣t−48.2∣=1.8, isolate the t variable by removing the absolute value.

Step-by-step explanation:

The correct answer is option d. Slowest runner's time: 46.2 seconds.

To solve the equation ∣t−48.2∣=1.8, we isolate the t variable by removing the absolute value. Since the absolute value is equal to 1.8, t can be either positive 1.8 away from 48.2 or negative 1.8 away from 48.2.

t - 48.2 = 1.8 or t - 48.2 = -1.8.

Simplifying the equations, we get:

t = 50 or t = 46.4.

The fastest runner's time can be 50 seconds, while the slowest runner's time can be 46.4 seconds. However, since we need to account for the slowest runner's time being 1.8 seconds slower than the team average of 49.2 seconds, the slowest runner's time can be calculated as:

49.2 - 1.8 = 47.4 seconds.

Therefore, the slowest runner's time is actually 46.2 seconds.