Question

Every week, Tiana runs 3 miles and records how long it takes to complete the run. She also records the change in time from the previous week. Last week her time increased by 2. Which integer could represent this change?

a) -2
b) 2
c) -1
d) 1

Answer 1

Tiana's time increase is represented by the integer 2, indicating a longer duration than the previous week. For displacement and distance while jogging, displacement is the overall change in her position, and distance is the sum of the lengths of her paths.

Step-by-step explanation:

Last week, Tiana's time increased by 2, which means it took her longer to complete her run compared to the previous week. An increase in time implies a positive change. Therefore, the integer that could represent this change is b) 2.

In the case of Tiana jogging along a straight path and turning back, the displacement is the overall change in position, while the distance is the total length of the path she jogged. If Tiana's original direction is considered positive, she first jogs 1.5 km, then jogs -2.4 km (in the opposite direction), and finally jogs +0.7 km in the original direction. Displacement equals 1.5 km - 2.4 km + 0.7 km, which simplifies to -0.2 km. The negative sign indicates that her final position is 0.2 km in the direction opposite to her starting direction. The distance she jogged is the absolute value of these, adding up to 1.5 km + 2.4 km + 0.7 km, which is 4.6 km.