9.5 Telling Time, Elapsed Time, & Money Calculations
Key Takeaways
- Time is a base-60 system, so 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes, and 2 hours 45 minutes as a decimal is 2.75 hours.
- The reliable method for elapsed time is counting up in friendly chunks — to the next hour, then whole hours, then the remaining minutes.
- Crossing noon or midnight requires converting to a 24-hour clock or splitting the interval at 12:00 to avoid the single most common elapsed-time error.
- Money problems combine decimal arithmetic with making change, and the counting-up method that works for time works identically for change.
Telling Time, Elapsed Time, & Money Calculations
The DRC content specification for Level E asks candidates to "tell and write time to the nearest minute and measure time intervals in minutes" and to "solve word problems involving addition and subtraction of time intervals in minutes." Level M extends this to multi-step measurement problems involving intervals of time and money. These are among the most common item contexts on the lower levels, and they trip up learners who are perfectly comfortable with decimals — because time is not base ten.
Time Is Base 60
| Unit relationship | Value |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes |
| 1 day | 24 hours |
| 1 week | 7 days |
| 1 year | 52 weeks, or 365 days |
The Level D and Level A reference sheets provide 1 hour = 60 minutes and 1 minute = 60 seconds. Everything else you supply.
The base-60 trap. $1.5$ hours is 1 hour 30 minutes, because 0.5 of 60 minutes is 30. It is not 1 hour 50 minutes. Likewise $2.25$ hours is 2 hours 15 minutes, and $0.4$ hours is $0.4 \times 60 = 24$ minutes.
Converting minutes to decimal hours (payroll form)
| Clock time | Decimal hours |
|---|---|
| 3 h 15 min | $3 + \tfrac{15}{60} = 3.25$ |
| 6 h 45 min | $6 + \tfrac{45}{60} = 6.75$ |
| 7 h 20 min | $7 + \tfrac{20}{60} \approx 7.33$ |
| 4 h 10 min | $4 + \tfrac{10}{60} \approx 4.17$ |
Payroll always uses decimal hours, so a timesheet showing 38 h 30 min is 38.5 hours for pay purposes.
Elapsed Time: The Counting-Up Method
Subtracting clock times directly invites regrouping errors. Count up in chunks instead.
From 9:40 a.m. to 2:15 p.m.
| Chunk | From → To | Time added |
|---|---|---|
| To the next hour | 9:40 → 10:00 | 20 min |
| Whole hours | 10:00 → 2:00 | 4 h |
| Remaining minutes | 2:00 → 2:15 | 15 min |
| Total | 4 h 35 min |
The method never requires borrowing across a base-60 boundary, and it works just as well across noon or midnight — which is exactly where direct subtraction fails.
Crossing midnight
A night shift runs from 10:45 p.m. to 6:30 a.m.
| Chunk | Time added |
|---|---|
| 10:45 p.m. → 11:00 p.m. | 15 min |
| 11:00 p.m. → 6:00 a.m. | 7 h |
| 6:00 a.m. → 6:30 a.m. | 30 min |
| Total | 7 h 45 min |
Working backward from a deadline
A cake bakes for 55 minutes and must cool 40 minutes before a 3:10 p.m. event. When must it go in the oven?
Total time needed: $55 + 40 = 95$ minutes $= 1$ h 35 min. Count back from 3:10 p.m.: 1 hour earlier is 2:10 p.m., 35 minutes earlier is 1:35 p.m.
Adding several intervals
Add minutes and hours separately, then regroup any minutes over 60.
1 h 50 min + 2 h 35 min + 45 min
Hours: $1 + 2 = 3$. Minutes: $50 + 35 + 45 = 130$. $130 \text{ min} = 2$ h 10 min, so the total is $3 + 2 = \mathbf{5}$ h 10 min.
Money
Money is decimal arithmetic with two fixed places and a currency label. Every rule from Section 2.2 applies, plus two habits:
- Line up the decimal points, always, on paper.
- Round to the nearest cent at the end, never in the middle. Rounding $0.4166$ to $0.42 before multiplying by 12 produces a different answer than multiplying first.
Making change by counting up
An item costs $13.47. The customer pays with a $20 bill.
| Count up | Amount |
|---|---|
| $13.47 → $13.50 | $0.03 |
| $13.50 → $14.00 | $0.50 |
| $14.00 → $20.00 | $6.00 |
| Change | $6.53 |
Same technique as elapsed time, applied to a different base.
Multi-step money problems
A caterer buys 3 trays at $18.75 each and 4 gallons of juice at $6.29 each. She pays with $100. What is her change?
- Trays: $3 \times 18.75 = $56.25$
- Juice: $4 \times 6.29 = $25.16$
- Subtotal: $56.25 + 25.16 = $81.41$
- Change: $100.00 - 81.41 = \mathbf{$18.59}$
Estimate to check: about $3 \times 19 = 57$ and $4 \times 6 = 24$, so roughly $81 spent and $19 back. The exact answer of $18.59 is confirmed.
Unit price comparisons
Which is the better buy: 24 oz for $4.56, or 32 oz for $5.76?
The 32-ounce package is the better value at 18 cents per ounce. Divide price by quantity — the smaller number wins.
A delivery driver begins a route at 8:35 a.m. and finishes at 4:20 p.m. How long was the route?
A timesheet shows 6 hours 45 minutes worked. At $19.20 per hour, what is the gross pay for that shift?
A customer buys 2 filters at $12.85 each and a bottle of cleaner for $7.49, then pays with two $20 bills. How much change is due?