⁵/₁₂ hours
Further explanation
Given:
- Jean-Luc jogged around the lake in \(1 \frac{1}{4}\) hour.
- William jogged the same distance in \(\frac{5}{6}\) hour.
Question:
How much longer did Jean-Luc take than William in hours?
The Process:
Let us prepare \(\boxed{1\frac{1}{4} = \frac{5}{4}}\) as a jogging time from Jean-Luc.
We have to do a subtraction between two fractions to find out how much longer did Jean-Luc take than William in hours.
Previously, we must equate the denominator. We know that the least common multiple (LCM) of 4 and 6 is 24.
- \(\boxed{ \ Jean-Luc: 1\frac{1}{4} = \frac{5}{4} = \frac{5 \times 6}{4 \times 6} = \frac{30}{24} \ }\)
- \(\boxed{ \ William: \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \ }\)
SInce \(\boxed{\frac{30}{24} > \frac{20}{24}}\), then Jean-Luc takes longer than William.
Let us calculate the subtraction between these two fractions.
\(\boxed{ \ 1\frac{1}{4} - \frac{5}{6} = \ ? \ }\)
\(\boxed{ \ = \frac{5}{4} - \frac{5}{6} \ }\)
\(\boxed{ \ = \frac{5 \times 6}{4 \times 6} - \frac{5 \times 4}{6 \times 4} = \ }\)
\(\boxed{ \ = \frac{30}{24} - \frac{20}{24} \ }\)
\(\boxed{ \ = \frac{30 - 20}{24} \ }\)
\(\boxed{ \ = \frac{10}{24} \ }\)
Simplify it. The numerator and denominator are divided by two.
\(\boxed{\boxed{ \ \frac{5}{12} \ }}\)
Thus, Jean-Luc takes \(\frac{5}{12}\) hours longer than William.
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Keywords: Jean-Luc jogged, around the lake, in 1 ¹/₄ hour, William, the same distance, in ⁵/₆, how much, longer, take than, in hours, least common multiple, LCM, ⁵/₁₂ hours
