Measurement & Time

Problem

Express minutes as fractions of an hour

Mia's trip is made of three parts: a train ride of 2 5/6 hours, a 20-minute bus ride, and a 1/12-hour walk. We need the total time of the whole trip, written in hours and minutes.
FractionsMeasurement & data
Your answer
How to solve
Strategy Analyze the Units — The three times use mismatched units, so the key move is a units analysis: rewrite the 20-minute bus ride as a fraction of an hour so every part is in hours. Once the units match, the problem breaks into clean subproblems (convert, then add fractions with unlike denominators, then translate back to hours and minutes).
1STEP 1

Make every part use the same unit

An hour is 60 minutes, so 20 minutes is 20/60 = 1/3 of an hour.

20 min = 20/60 h = 1/3 h
2STEP 2

Write the train time as a single fraction

Turn the mixed number 2 5/6 into an improper fraction so all three parts are plain fractions ready to add.

2 5/6 = (2 × 6 + 5)/6 = 17/6 h
3STEP 3

Give the fractions a common denominator

To add 17/6, 1/3, and 1/12, rewrite them with the common denominator 12, since 12 is a multiple of 6, 3, and 12.

17/6 = 34/12, 1/3 = 4/12, 1/12 = 1/12
4STEP 4

Add the three times

Now that the denominators match, add the numerators to find the total in hours.

34/12 + 4/12 + 1/12 = 39/12 = 13/4 = 3 1/4 h
5STEP 5

Translate the leftover fraction back into minutes

Change the 1/4 hour into minutes so the answer is in hours and minutes.

1/4 h = 1/4 × 60 min = 15 min
Answer
3 hours 15 minutes
Check by working only in minutes: 2 5/6 h = 170 min, the bus is 20 min, and 1/12 h = 5 min, so 170 + 20 + 5 = 195 min = 3 h 15 min. This matches, and the magnitude is sensible: the trip is a bit over 3 hours, mostly the train.
Takeaway

Turn the odd-unit part (minutes) into a fraction of an hour first, then everything adds up neatly.

  • Make every part use the same unit
  • Write the train time as a single fraction
  • Give the fractions a common denominator
  • Add the three times
  • Translate the leftover fraction back into minutes
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