Route to 240 Oak: Direction, Distance, and a Water Main Break
You are in a marked unit stopped at Main Street and Park Avenue, facing east on Main. Dispatch assigns you a disturbance at 240 Oak Street, located on the east side of Oak, 0.1 mile north of Third Avenue. Grid facts: Main Street runs east–west and Park Avenue runs north–south; every block is 0.1 mile. Dispatch's route is: east on Main 0.6 mile to Elm Street; left (north) on Elm 0.6 mile to Third Avenue; right (east) on Third 0.3 mile to Oak Street. Elm and Washington Streets run north–south and are 0.5 mile apart. Main, Second Avenue, and Third Avenue run east–west, with Second 0.2 mile north of Main and Third 0.4 mile north of Second. A broadcast now reports Elm Street closed between Second and Third Avenues for a water main break, expected to last 45–60 minutes.
1. Ignoring the closure, what is the straight-line distance and compass bearing from Main and Park to 240 Oak Street, and which way will you be facing and looking when you arrive?
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Break the route into components.
- East: 0.6 mi (Main) + 0.3 mi (Third) = 0.9 mile east
- North: 0.6 mi (Elm) + 0.1 mi (Oak, north of Third) = 0.7 mile north
Straight-line distance (Pythagorean): √(0.9² + 0.7²) = √(0.81 + 0.49) = √1.30 ≈ 1.14 miles
Bearing relative to due east: arctan(0.7 ÷ 0.9) = arctan(0.778) ≈ 38° north of east (i.e., roughly northeast).
Arrival: You will be traveling northbound on Oak Street and the address is on the east side, which is your right. Do not confuse the grid displacement (1.14 mi) with driving distance (1.6 mi) - the street route is longer than the straight line because it zigzags.
2. Given the closure of Elm between Second and Third, give a compliant alternate route, its distance, and the extra distance over Dispatch's route.
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Original route: 0.6 + 0.6 + 0.3 + 0.1 = 1.6 miles.
With Elm blocked north of Second, you cannot use Elm above Second. Two equivalent detours exist:
Detour A (via Second and Washington): east on Main 0.6 → north on Elm 0.2 to Second (this leg is below the closure) → east on Second 0.5 to Washington → north on Washington 0.4 to Third → west on Third 0.2 to Oak → north on Oak 0.1. Total = 0.6 + 0.2 + 0.5 + 0.4 + 0.2 + 0.1 = 2.0 miles.
Detour B (stay on Main): east on Main 0.6 + 0.5 to Washington → north on Washington 0.6 to Third → west on Third 0.2 to Oak → north 0.1. Total = 0.6 + 0.5 + 0.6 + 0.2 + 0.1 = 2.0 miles.
Extra distance: 2.0 − 1.6 = 0.4 mile either way. Since both are equal, prefer Detour B: it keeps you on Main longer (better radio coverage, no turn off the arterial) and avoids a redundant turn onto Elm. Advise dispatch of the detour so backup units do not repeat the blocked route.
3. After you clear the call at 240 Oak, describe your return route to Main and Park, the total distance, and your heading as you turn onto Elm Street.
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Return route (reverse of the outbound legs):
- South on Oak 0.1 mile to Third Avenue.
- West (right) on Third 0.3 mile to Elm Street.
- South (left) on Elm 0.6 mile to Main Street.
- West (right) on Main 0.6 mile to Park Avenue.
Total: 0.1 + 0.3 + 0.6 + 0.6 = 1.6 miles - the same as the outbound route, because each leg is simply reversed.
Heading on turning onto Elm: you are westbound on Third, turning left, so you will be heading south on Elm. Confirm the closure status before relying on Elm; if the water main break is still active, use Washington instead (0.1 south on Oak → 0.3 west on Third → 0.6 south on Washington → 0.5 west on Main = 1.5 miles).
Check your mindset: after the call, it is easy to retrace from memory and turn the wrong way off a one-way or onto a closed segment. State the route out loud before you put the car in gear.