Question

5

Drag the tiles to the correct boxes to complete the pairs.
Luke is driving from his house to the store. After driving 16 miles at a constant speed of 0.8 mile/minute, he realizes that he forgot his wallet. So,
he turns around and drives all the way back to his house at the same speed. The equation below models Luke's distance, in miles, from home as
he drives for t minutes.
d = -0.8t - 20 + 16
Using the given equation, match the number of minutes since Luke started driving from his house to his distance from the house.
12 minutes
27 minutes
31 minutes
7 minutes
10.4 miles on his return trip
5.6 miles on his trip to the restaurant
9.6 miles his trip to the restaurant
7.2 miles on his return trip

Answer 1

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

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