A Closed Block and a Dispatch Order That Cannot Be Followed
You are stopped at 3rd Avenue and Alder Street, facing north. Avenues run north–south, numbered 1st through 6th west to east, 0.2 mile apart. Streets run east–west and are named, south to north: Alder, Birch, Cedar, Dalles, Elm, each 0.1 mile apart. 3rd Avenue is one-way northbound; 4th Avenue is one-way southbound; all other avenues are two-way. A water main break has closed 3rd Avenue between Birch and Dalles. Average speed in the grid is 25 mph, and each signalized intersection costs about 20 seconds of stopped delay. At 09:05 dispatch transmits: 'Go north on 3rd to Cedar, east on Cedar three blocks to 6th, north on 6th two blocks to Elm, then west on Elm four blocks and stage for the detail.'
1. Can you execute the instruction as given? Explain, then give the shortest legal alternate route to the same staging point with its total distance.
Read the worked answer
No. Cedar lies between Birch and Dalles, which is exactly the stretch of 3rd Avenue that is closed. The order is unexecutable as written, and the useful thing is to say so out loud on the radio rather than discover it at a barricade.
Staging point from the original order: four blocks west on Elm from 6th puts you at 2nd Avenue and Elm Street, facing west. The destination is valid; only the path is broken.
Shortest legal alternate (1.8 miles):
- North on 3rd from Alder to Birch - 1 block, 0.1 mi (Birch is the closure boundary, so you can reach it but not cross it).
- East on Birch from 3rd to 5th - 2 blocks, 0.4 mi. You cannot use 4th, because 4th is one-way southbound.
- North on 5th from Birch to Cedar - 1 block, 0.1 mi. 5th is two-way.
- East on Cedar from 5th to 6th - 1 block, 0.2 mi.
- North on 6th from Cedar to Elm - 2 blocks, 0.2 mi.
- West on Elm from 6th to 2nd - 4 blocks, 0.8 mi.
Total: 0.1 + 0.4 + 0.1 + 0.2 + 0.2 + 0.8 = 1.8 miles, ending at 2nd and Elm facing west.
One equally short variant exists: east on Alder from 3rd to 5th (0.4), then north on 5th from Alder to Cedar (0.2), then the same remaining legs - also 1.8 miles, and it crosses one fewer signal. If you are relaying this to another unit, name the closure explicitly, because the obvious route is the blocked one.
2. Compute the travel time for the route you chose, including signal delay, and state your estimated arrival time. Show the arithmetic and state your assumptions.
Read the worked answer
Travel time at speed: 1.8 miles ÷ 25 mph = 0.072 hours = 4.32 minutes, or about 4 minutes 19 seconds.
Signal delay: count the signalized intersections actually crossed, once each, with no double-counting at corners where you turn:
- Cedar and 5th
- Cedar and 6th
- 6th and Dalles
- 6th and Elm
- Elm and 5th
- Elm and 4th
- Elm and 3rd
- Elm and 2nd
That is 8 signals × 20 seconds = 160 seconds = 2 minutes 40 seconds.
Total: 4:19 + 2:40 = 6 minutes 59 seconds, call it 7 minutes. Departing at 09:05, you stage at approximately 09:12.
Assumptions to state on the radio: no traffic congestion beyond signal delay, no pedestrian or train delay, and the 25 mph figure is an average rather than a limit you can exceed. If you take the Alder variant instead, you cross 7 signals rather than 8, saving about 20 seconds - a difference too small to matter for staging but worth knowing if the detail is time-critical.
Note the practical point: the arithmetic says 09:12, but you should call your arrival at the closure or the turn onto Elm rather than announcing a precise ETA you cannot guarantee. Dispatch needs to know where you are, not how well you divide.
3. From the staging point at 2nd and Elm facing west, dispatch reassigns you to 5th and Alder. Give the shortest legal route and distance, and explain the constraint that shapes the answer.
Read the worked answer
The constraint is that 3rd Avenue runs northbound only, so the natural instinct - go east to 3rd and turn south - is illegal and would put you head-on into northbound traffic. The two legal options tie on distance.
Option 1, via 2nd Avenue (1.0 mile): south on 2nd from Elm to Alder - 4 blocks × 0.1 = 0.4 mi - then east on Alder from 2nd to 5th - 3 blocks × 0.2 = 0.6 mi. Total 1.0 mi.
Option 2, via 4th Avenue (1.0 mile): east on Elm from 2nd to 4th - 2 blocks × 0.2 = 0.4 mi - south on 4th from Elm to Alder - 4 blocks × 0.1 = 0.4 mi - east on Alder from 4th to 5th - 1 block × 0.2 = 0.2 mi. Total 1.0 mi.
Recommendation: Option 1. Equal distance, but two turns instead of three, and it starts from the direction you are already facing - a U-turn is not required, and a U-turn on a two-way street with a signal at the next corner is an unnecessary risk under code-3 pressure.
Two habits worth carrying from this: always check the one-way before the shortest path, and when two routes tie on distance, break the tie on turns, signals, and which direction you are already pointed.