Problem 10 · 2004 AMC 8
Easy
Arithmetic & Operations
time-conversionrate
Handy Aaron helped a neighbor 114 hours on Monday, 50 minutes on Tuesday, from 8:20 to 10:45 on Wednesday morning, and a half-hour on Friday. He is paid $3 per hour. How much did he earn for the week?
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Answer: E — $15.
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Hint 1 of 2
Everything is in different units (hours, minutes, a clock span). Pick one currency — minutes — and convert every day into it before adding anything. Mixing units is the only thing that makes this problem hard.
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Hint 2 of 2
The discipline is convert to a common unit first: get all times into minutes, total them, convert once to hours, then apply the rate. One conversion at the end beats four fiddly fraction additions.
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Approach: total the minutes, then pay
- Convert each day to minutes: Mon 1¼ hr = 75, Tue = 50, Wed 8:20–10:45 = 2 hr 25 min = 145, Fri ½ hr = 30.
- Add: 75 + 50 + 145 + 30 = 300 minutes = exactly 5 hours. Working in minutes keeps everything a whole number — no common denominators needed.
- Pay: 5 hr × $3/hr = $15.
- Sanity check: the four chunks are each roughly an hour, summing to about 5 hours × $3 ≈ $15 — the largest choice, which fits.
Another way — add the fractions of an hour:
- In hours: 5/4 + 5/6 + 29/12 + 1/2. Over 12ths: 15/12 + 10/12 + 29/12 + 6/12 = 60/12 = 5 hr.
- Earnings: 3 × 5 = $15.
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