Question

5

Answer 1

Answer:

10.4 miles on his return trip → 27 minutes

5.6 miles on his trip to the restaurant → 7 minutes

9.6 miles on his trip to the restaurant → 12 minutes

7.2 miles on his return trip → 31 minutes

Step-by-step explanation:

When solving, we note that on his trip to the restaurant, $\left |t - 20 \right |$ is a negative number, while it is a positive number on his return trip

1) At 10.4 miles on his return trip, we have;

$d = 10.4 = -0.8 \cdot \left |t - 20 \right |+ 16$

Therefore;

(10.4 - 16)/(-0.8) = 7 =  $\left |t - 20 \right |$

t = 20 + 7 = 27

The number of minutes since Luke started driving from his house, t = 27 minutes

2) At 5.6 miles on his trip to the restaurant, we have;

$d = 5.6 = -0.8 \cdot \left |t - 20 \right |+ 16$

Therefore;

(5.6 - 16)/(-0.8) = 13 =  $\left |t - 20 \right |$

Here, t is less than 20 (minutes), therefore, t - 20 is negative, we get

t - 20 = -13

∴ t = 20+ (-13) = 7

The number of minutes since Luke started driving from his house when he is 5.6 miles on his trip to the restaurant, t = 7 minutes

3) At 9.6 miles on his trip to the restaurant, we have;

$d = 9.6 = -0.8 \cdot \left |t - 20 \right |+ 16$

Therefore;

(9.6 - 16)/(-0.8) = 8 =  $\left |t - 20 \right |$

$\left |t - 20 \right |$ is negative on his trip to the restaurant, therefore;

- $\left |t - 20 \right |$ = 8

t - 20 = -8

t = 20 - 8 = 12

The number of minutes since he started driving from his house to when he is 9.6 miles on the his trip to the restaurant, t = 12 minutes

4) At 7.2 miles on his return trip, we have;

$d = 7.2 = -0.8 \cdot \left |t - 20 \right |+ 16$

Therefore;

(7.2 - 16)/(-0.8) = 11 =  $\left |t - 20 \right |$

t = 20 + 11 = 31

At 7.2 miles from his house on the return trip, t = 31 minutes