Question

1. paige got directions to her friends house. when she started her trip to see her friend, her odometer read 10, 119 miles. the directions said to turn right in 3.4 miles, turn left in 5.2 miles, and turn left again in 1.9 miles. which of the following has the correct odometer reading for the correct turn?

the odometer will read 10, 129.5 miles when she needs to make the first left turn.
the odometer will read 10, 124.3 miles when she needs to make the first left turn.
the odometer will read 10, 129.5 miles when she needs to make the second left turn.
the odometer will read 10, 124.2 miles when she needs to make the right turn.

Explanation:

Step1: Calculate odometer for right turn

Initial odometer: \(10,119\) miles. Distance to right turn: \(3.4\) miles.
Odometer at right turn: \(10119 + 3.4 = 10122.4\) miles.

Step2: Calculate odometer for first left turn

After right turn, add \(5.2\) miles (to first left turn).
Odometer: \(10122.4 + 5.2 = 10127.6\) miles? Wait, no—wait, initial + right turn + first left turn? Wait, directions: turn right in \(3.4\) miles, turn left in \(5.2\) miles (after right turn?), then turn left again in \(1.9\) miles. Wait, re-express:

First turn: right at \(3.4\) miles: odometer \(10119 + 3.4 = 10122.4\).

Then, left turn in \(5.2\) miles after start? No, the directions: "turn right in \(3.4\) miles, turn left in \(5.2\) miles, and turn left again in \(1.9\) miles"—probably cumulative. So:

• Right turn: \(10119 + 3.4 = 10122.4\) (so option 4: \(10,124.2\) is wrong, since \(10119 + 3.4 = 10122.4\)).

• First left turn: \(10119 + 3.4 + 5.2 = 10119 + 8.6 = 10127.6\)? Wait, no—maybe the "turn left in \(5.2\) miles" is from start? Wait, the options: let's check each option.

Option 1: first left turn (after right and then left? No, first left turn: total distance \(3.4 + 5.2 = 8.6\)? Wait, no—wait, the options:

Option 3: second left turn: total distance \(3.4 + 5.2 + 1.9 = 10.5\). Initial: \(10119 + 10.5 = 10129.5\). Ah! So:

• Right turn: \(3.4\) miles: \(10119 + 3.4 = 10122.4\) (option 4 is \(10,124.2\) → wrong).

• First left turn: \(3.4 + 5.2 = 8.6\) miles: \(10119 + 8.6 = 10127.6\) → options 1 and 2: \(10,129.5\) and \(10,124.3\) → both wrong.

• Second left turn: \(3.4 + 5.2 + 1.9 = 10.5\) miles: \(10119 + 10.5 = 10129.5\). So option 3: "The odometer will read 10, 129.5 miles when she needs to make the second left turn." is correct.

Answer:

The odometer will read 10, 129.5 miles when she needs to make the second left turn.