2.2 Elapsed time, scheduling & production rates

Working with Time on the Job

Time problems show up constantly in workplace math: when does a shift end, how long did a task take, how many parts can a line produce before lunch? These questions test elapsed time (how much time passes between two clock readings) and rate (how fast work gets done).

Elapsed Time Basics

Elapsed time is the difference between a start time and an end time. The tricky part is that clocks are base 60, not base 10 - there are 60 minutes in an hour, not 100. When subtracting, you often need to "borrow" 60 minutes from an hour.

Example. A delivery starts at 9:50 AM and ends at 11:15 AM. How long did it take?

• From 9:50 to 11:50 is 2 hours.
• But we only need to reach 11:15, which is 35 minutes before 11:50.
• So the time is 2 hours - 35 minutes = 1 hour 25 minutes.

You can also add up in steps: 9:50 to 10:00 is 10 minutes; 10:00 to 11:00 is 1 hour; 11:00 to 11:15 is 15 minutes. Total = 1 hour 25 minutes.

Crossing Noon and Midnight

AM/PM problems trip people up when the clock passes 12:00. A dependable method is to count to 12:00 first, then continue past it.

Example. A machine runs from 10:30 AM to 2:15 PM.

• 10:30 AM to 12:00 noon = 1 hour 30 minutes.
• 12:00 noon to 2:15 PM = 2 hours 15 minutes.
• Total = 3 hours 45 minutes.

Crossing midnight, common on night shifts, works the same way.

Example. A security guard's shift runs from 10:00 PM to 6:00 AM.

• 10:00 PM to 12:00 midnight = 2 hours.
• 12:00 midnight to 6:00 AM = 6 hours.
• Total = 8 hours.

Scheduling

Scheduling questions ask you to add a duration to a start time, or to fit tasks into an available window.

Example. A meeting begins at 1:45 PM and lasts 90 minutes. When does it end? 90 minutes is 1 hour 30 minutes. 1:45 + 1:00 = 2:45; 2:45 + 0:30 = 3:15 PM.

Example (working backward). A shipment must be finished by 5:00 PM and the packing job takes 2 hours 30 minutes. When must the crew start? Subtract the duration from the deadline: 5:00 - 2:30 = 2:30 PM. Working backward from a deadline is just elapsed time in reverse.

Example. A technician has from 8:00 AM to 12:00 noon (4 hours = 240 minutes) and each service call takes 35 minutes. How many calls fit? 240 divided by 35 = 6.85..., so 6 complete calls fit (the 7th would not finish in time). This is a place where you round down, because a partial call does not count.

Production and Work Rates

A rate connects an amount of work to the time it takes. The three core relationships are:

Rate = units / time Units = rate x time Time = units / rate

Example (rate). A press stamps 450 parts in 6 hours. Its rate is 450 divided by 6 = 75 parts per hour.

Example (units). At 75 parts per hour, how many parts in an 8-hour shift? 75 x 8 = 600 parts.

Example (time). An order calls for 1,200 parts. At 75 parts per hour, the time needed is 1,200 divided by 75 = 16 hours.

Combining Rates and Elapsed Time

Real questions often chain these ideas together.

Example. A bottling line fills 240 bottles per hour and runs from 7:00 AM to 11:30 AM. How many bottles?

• Elapsed time: 7:00 to 11:30 = 4 hours 30 minutes = 4.5 hours.
• Bottles: 240 x 4.5 = 1,080 bottles.

Notice the 30 minutes had to be converted to 0.5 hour before multiplying - mixing "4 hours 30" with a per-hour rate is a frequent error.

Two-Worker Rates

Some problems combine the output of more than one worker or machine. Add their hourly rates to get a combined rate.

Example. Worker A assembles 12 units per hour and Worker B assembles 18 units per hour. Together they make 12 + 18 = 30 units per hour. To fill an order of 210 units: 210 divided by 30 = 7 hours.

Quick Reference

Always convert minutes to a fraction of an hour (30 min = 0.5, 15 min = 0.25, 45 min = 0.75) before multiplying by an hourly rate, and round down when counting how many whole tasks fit into a fixed window. Those two habits catch the errors these questions are specifically designed to expose on the job floor.