5.2 ETA & Response-Time Calculations

Why ETA and Response-Time Math Matter

ETA (Estimated Time of Arrival) and response-time calculations are the single most frequently tested "real-life scenario" flavor of CritiCall's Numerical Ability module, and they are also a genuine daily dispatcher task: giving a caller an honest arrival estimate, logging response times for agency compliance reporting, and choosing between two available units based on whose travel time is shorter. Where Section 5.1 covered the general arithmetic types, this section drills the specific clock-and-distance math that shows up on almost every CritiCall numerical item bank.

Core Terms and the Response-Time Timeline

A dispatched call runs through a sequence of timestamped phases, and CritiCall items frequently ask you to calculate the interval between two of them rather than the whole call:

Response time, in its most common test usage, is the interval from dispatch to arrival on scene — arrival time minus dispatch time. Some items narrow the question to just the travel-time segment, so always confirm which two timestamps (or which two events) the question is actually asking you to subtract.

CritiCall items present times in 24-hour ("military") clock format, matching real computer-aided dispatch (CAD) systems — for example, 14:18 means 2:18 PM and 23:55 means 11:55 PM. Two clock facts drive almost every mistake on this topic: an hour has 60 minutes, not 100, so subtraction across an hour boundary requires "borrowing" 60 rather than 100; and a time that rolls past 24:00 belongs to the next calendar day, so the elapsed-time calculation must add 24 hours' worth of minutes before subtracting.

Core Formulas

• ETA = Dispatch Time + Travel Time
• Travel Time (minutes) = (Distance ÷ Speed) × 60
• Response Time = Arrival Time − Dispatch Time (clock subtraction, watching for hour/day rollovers)
• Average Speed = Distance ÷ Time

Worked Examples

Example 1 — Same-Hour Elapsed Time. A unit is dispatched at 08:47 and arrives 6 minutes later. What is the arrival time? 08:47 + 0:06 = 08:53.

Example 2 — Crossing the Hour (Borrowing 60, Not 100). A unit is dispatched at 21:53 and arrives at 22:07. What is the response time?

• Step 1: From 21:53 to 22:00 is 7 minutes (60 − 53 = 7).
• Step 2: From 22:00 to 22:07 is 7 more minutes.
• Step 3: 7 + 7 = 14 minutes.

Example 3 — Crossing Midnight. A unit is dispatched at 23:48 and arrives at 00:05 the next day. What is the response time?

• Step 1: Treat 00:05 as 24:05 for the subtraction.
• Step 2: 24:05 − 23:48 = 0:17 = 17 minutes.

Example 4 — Distance/Speed to ETA. A unit is 14 miles from a call, dispatched at 10:10, and can average 35 mph. What is the ETA?

• Step 1: Travel time (hours) = 14 ÷ 35 = 0.4 hours.
• Step 2: Convert to minutes = 0.4 × 60 = 24 minutes.
• Step 3: ETA = 10:10 + 0:24 = 10:34.

Example 5 — Required Average Speed. A unit must cover 20 miles in 25 minutes to meet a hospital's trauma-window deadline. What average speed is required?

• Step 1: Convert 25 minutes to hours: 25 ÷ 60 ≈ 0.417 hours.
• Step 2: Speed = Distance ÷ Time = 20 ÷ 0.417 ≈ 48 mph.

Realistic Exam Scenario

A CritiCall item might ask you to compare two units: "Unit 12 is 9 miles away averaging 45 mph. Unit 7 is 6 miles away averaging 20 mph. Which unit has the shorter ETA, and by how many minutes?" Unit 12: 9 ÷ 45 = 0.2 hr = 12 minutes. Unit 7: 6 ÷ 20 = 0.3 hr = 18 minutes. Unit 12 arrives first, 6 minutes sooner — the kind of comparison a real dispatcher makes in seconds before keying up the radio.

Common Traps

• Treating the clock like a decimal. 23:55 is not "23.55" — minutes wrap at 60, so 23:55 + 0:10 = 00:05 the next day, not 24.05 read as hours-and-hundredths.
• Forgetting to borrow 60 across an hour boundary, leading to a response time that is off by exactly the size of the borrowing error.
• Missing a midnight rollover, which produces a negative or nonsensical elapsed time unless you add 24 hours to the next-day timestamp first.
• Answering the wrong interval — confirm whether the question wants total response time (dispatch to arrival) or just travel time, since some items isolate one phase.

Quick Takeaways

• ETA = Dispatch Time + Travel Time, and Travel Time (minutes) = (Distance ÷ Speed) × 60 — memorize both formulas cold.
• CritiCall uses 24-hour clock notation matching real CAD systems; an hour is 60 minutes, and times past 24:00 roll into the next day.
• Always identify which two timestamps or phases (dispatch-to-arrival vs. travel-only) a question is actually asking you to subtract.
• Crossing-the-hour and crossing-midnight problems are the two most common sources of an off-by-a-fixed-amount wrong answer — practice both patterns deliberately.
• When comparing two units' ETAs, compute each unit's travel time independently before comparing — do not average distances or speeds together.