Identifying Highest Time Taken for Task Completion

The times taken by four persons A, B, C, and D to complete a task are given as fractions of an hour:

• Person A: $\frac{2}{3}$ h
• Person B: $\frac{3}{4}$ h
• Person C: $\frac{4}{5}$ h
• Person D: $\frac{1}{5}$ h

To find who took the highest amount of time, we need to compare these fractions.

Comparing Task Completion Times

We can compare the fractions by converting them to decimals or by finding a common denominator. Using a common denominator is effective here.

The denominators are 3, 4, and 5. The least common multiple (LCM) of 3, 4, and 5 is 60.

Convert each fraction to an equivalent fraction with a denominator of 60:

• A: $\frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60}$ h
• B: $\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}$ h
• C: $\frac{4}{5} = \frac{4 \times 12}{5 \times 12} = \frac{48}{60}$ h
• D: $\frac{1}{5} = \frac{1 \times 12}{5 \times 12} = \frac{12}{60}$ h

Determining the Maximum Time

Now, compare the numerators of these equivalent fractions:

• 40 (for A)
• 45 (for B)
• 48 (for C)
• 12 (for D)

The largest numerator is 48, which corresponds to Person C.

Therefore, Person C took the highest amount of time ($\frac{48}{60}$ h or $\frac{4}{5}$ h) to complete the task.