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, [tex]\left |t - 20 \right |[/tex] 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;
[tex]d = 10.4 = -0.8 \cdot \left |t - 20 \right |+ 16[/tex]
Therefore;
(10.4 - 16)/(-0.8) = 7 = [tex]\left |t - 20 \right |[/tex]
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;
[tex]d = 5.6 = -0.8 \cdot \left |t - 20 \right |+ 16[/tex]
Therefore;
(5.6 - 16)/(-0.8) = 13 = [tex]\left |t - 20 \right |[/tex]
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;
[tex]d = 9.6 = -0.8 \cdot \left |t - 20 \right |+ 16[/tex]
Therefore;
(9.6 - 16)/(-0.8) = 8 = [tex]\left |t - 20 \right |[/tex]
[tex]\left |t - 20 \right |[/tex] is negative on his trip to the restaurant, therefore;
- [tex]\left |t - 20 \right |[/tex] = 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;
[tex]d = 7.2 = -0.8 \cdot \left |t - 20 \right |+ 16[/tex]
Therefore;
(7.2 - 16)/(-0.8) = 11 = [tex]\left |t - 20 \right |[/tex]
t = 20 + 11 = 31
At 7.2 miles from his house on the return trip, t = 31 minutes
