Question

Jimmy ran 40 meters west from home and then turned north to jog 15 meters. Jimmy ran 55 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?

42.7
912.5
15
8

Answer 1

To determine how many meters Jimmy could have jogged in a straight line to reach the same point, we can use the Pythagorean theorem.

1. **Find the coordinates of Jimmy's position:**
- He starts at home, which we can consider as the point (0, 0).
- After running 40 meters west, his position is (-40, 0).
- Then he jogs 15 meters north. Adding this vertical distance, his position becomes (-40, 15).

2. **Calculate the straight-line distance from the starting point to the final position:**
- We can use the Pythagorean theorem, where the straight-line distance \( d \) can be calculated as follows:
\[
d = \sqrt{(\text{{change in x}})^2 + (\text{{change in y}})^2}
\]
- Here, the change in x is -40 (from 0 to -40) and the change in y is 15 (from 0 to 15):
\[
d = \sqrt{(-40)^2 + (15)^2}
\]
\[
d = \sqrt{1600 + 225}
\]
\[
d = \sqrt{1825}
\]
\[
d \approx 42.7 \text{ meters}
\]

Therefore, Jimmy could have jogged approximately **42.7 meters** in a straight line to reach the same point.

So, the answer is **42.7**.