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Solve the following word problems: 1. Michael took 1 1/4 hours to do his homework. Henry took 1/2 hour more than Michael to do his homework. How long did Henry take to do his homework? 2. Alan wanted

Mathematics

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Here are the solutions to the word problems:

1. Michael took 1141\frac{1}{4} hours to do his homework. Henry took 12\frac{1}{2} hour more than Michael to do his homework. How long did Henry take to do his homework?

  1. Identify the given times.

    Michael's time: 1141\frac{1}{4} hours
    Henry's additional time: 12\frac{1}{2} hour

  2. Add Michael's time and Henry's additional time to find Henry's total time.

    114+121\frac{1}{4} + \frac{1}{2}

  3. Find a common denominator for the fractions.

    The least common denominator for 4 and 2 is 4.

    12=1×22×2=24\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}

  4. Add the fractions and the whole number.

    114+24=11+24=1341\frac{1}{4} + \frac{2}{4} = 1\frac{1+2}{4} = 1\frac{3}{4}

    Henry took \boxed{\text{1\frac{3}{4} hours}} to do his homework.

    2. Alan wanted to complete his project in 2 hours. He completed his project in 31103\frac{1}{10} hours instead. How much more time did he take to complete his project?

  5. Identify the planned and actual times.

    Planned time: 2 hours
    Actual time: 31103\frac{1}{10} hours

  6. Subtract the planned time from the actual time to find the difference.

    3110−23\frac{1}{10} - 2

  7. Subtract the whole numbers.

    3−2=13 - 2 = 1

  8. Combine the result with the fraction.

    1+110=11101 + \frac{1}{10} = 1\frac{1}{10}

    Alan took \boxed{\text{1\frac{1}{10} hours}} more time to complete his project.

    3. Mrs Davies bought 6256\frac{2}{5} kilograms of flour and 2582\frac{5}{8} kilograms of sugar. What was the total mass of the flour and sugar she bought?

  9. Identify the masses of flour and sugar.

    Flour: 6256\frac{2}{5} kg
    Sugar: 2582\frac{5}{8} kg

  10. Add the masses to find the total mass.

    625+2586\frac{2}{5} + 2\frac{5}{8}

  11. Add the whole numbers.

    6+2=86 + 2 = 8

  12. Find a common denominator for the fractions 25\frac{2}{5} and 58\frac{5}{8}.

    The least common multiple of 5 and 8 is 40.

    25=2×85×8=1640\frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} 58=5×58×5=2540\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}

  13. Add the fractions.

    1640+2540=16+2540=4140\frac{16}{40} + \frac{25}{40} = \frac{16+25}{40} = \frac{41}{40}

  14. Convert the improper fraction to a mixed number.

    4140=1140\frac{41}{40} = 1\frac{1}{40}

  15. Add this mixed number to the sum of the whole numbers from Step 3.

    8+1140=91408 + 1\frac{1}{40} = 9\frac{1}{40}

    The total mass of the flour and sugar she bought was \boxed{\text{9\frac{1}{40} kg}}.

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