Javier and Stella are planning their exercise routines. Javier and Stella have a body mass of 70 kg and 60 kg respectively. The speed for walking and jogging of the two individuals are represented in the chart.

  1. (a)

    In their first week of exercise, they each plan to go for four brisk walks.

    They will walk the same route each time.

    The four walks together meet the minimum target for the time for optimal health benefits in one week.

    1. (i)

      Find the distance of one of these walks.

      Answer ... km

    2. (ii)

      Find out how many more calories Javier burns in these four walks than Stella.

      Answer ... calories

  2. (b)

    After one month, they change their routines.

    Javier wants to gain additional health benefits.

    He decides to do a 4 km walk 3 times per week and do a 6 km jog 2 times per week.

    He will also attend a 45-minute yoga class 2 times per week.

    Stella wants to maintain optimal health benefits.

    She decides to do an 8 km jog 2 times per week.

    She will also attend a 30-minute weight training session 2 times per week.

    Javier says:

    We will both meet our targets for exercise.

    However, I will burn about 50% more calories than Stella during our exercise per week.

    Is Javier correct?

    Justify your decision with clear calculations.

    Answer space for 10 (b)

    Javier is ...
    ...

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Worked solution

10(a)(ii)

1. Find the total calories burned by each person for the four brisk walks and compare them.

The four walks together take 150150 minutes.

Since 150÷30=5150 \div 30 = 5, multiply the 30-minute calorie values by 55.

Using the Walking 6.56.5 km/h row:

Javier, 7070 kg: 150×5=750150 \times 5 = 750 calories

Stella, 6060 kg: 130×5=650130 \times 5 = 650 calories

Difference:
750−650=100750 - 650 = 100

Answer

100100 calories

10(b)

1. Check whether Javier meets the target for additional health benefits.

For Javier's walks:
time for one walk=46 h=23 h=40 min\text{time for one walk}=\frac{4}{6}\text{ h}=\frac{2}{3}\text{ h}=40\text{ min}
total walking time=3×40=120 min\text{total walking time}=3\times 40=120\text{ min}

For Javier's jogs:
time for one jog=68 h=0.75 h=45 min\text{time for one jog}=\frac{6}{8}\text{ h}=0.75\text{ h}=45\text{ min}
total jogging time=2×45=90 min\text{total jogging time}=2\times 45=90\text{ min}

Since 11 min vigorous =2=2 min moderate,
90 min jogging=180 min moderate-equivalent90\text{ min jogging}=180\text{ min moderate-equivalent}

Total moderate-equivalent time:
120+180=300 min120+180=300\text{ min}

So Javier meets the target for additional health benefits.

2. Check whether Stella meets the target for optimal health benefits.

For Stella's jogs:
time for one jog=810 h=0.8 h=48 min\text{time for one jog}=\frac{8}{10}\text{ h}=0.8\text{ h}=48\text{ min}
total jogging time=2×48=96 min\text{total jogging time}=2\times 48=96\text{ min}

Stella needs at least 7575 min of vigorous-intensity aerobic activity.

Since 96>7596>75, Stella meets the target for optimal health benefits.

3. Calculate Javier's total calories burned per week.

Javier has mass 7070 kg.

Walking calories: use Walking 6.56.5 km/h, 7070 kg: 150150 calories per 3030 min.
walking calories=12030×150=600\text{walking calories}=\frac{120}{30}\times 150=600

Jogging calories: use Jogging 88 km/h, 7070 kg: 280280 calories per 3030 min.
jogging calories=9030×280=840\text{jogging calories}=\frac{90}{30}\times 280=840

Yoga calories:
45 min×2=90 min=1.5 h45\text{ min}\times 2=90\text{ min}=1.5\text{ h}
yoga calories=1.5×3×70=315\text{yoga calories}=1.5\times 3\times 70=315

Total calories burned by Javier:
600+840+315=1755600+840+315=1755

4. Calculate Stella's total calories burned per week.

Stella has mass 6060 kg.

Jogging calories: use Jogging 9.59.5 km/h, 6060 kg: 300300 calories per 3030 min.
jogging calories=9630×300=960\text{jogging calories}=\frac{96}{30}\times 300=960

Weight training calories:
30 min×2=60 min=1 h30\text{ min}\times 2=60\text{ min}=1\text{ h}
weight training calories=1×4×60=240\text{weight training calories}=1\times 4\times 60=240

Total calories burned by Stella:
960+240=1200960+240=1200

5. Compare Javier's calories with Stella's and decide whether Javier's statement is correct.

Difference in calories:
1755−1200=5551755-1200=555

Percentage more than Stella:
5551200×100%=46.25%\frac{555}{1200}\times 100\%=46.25\%

This is about 50%50\% more.

Both also do muscle-strengthening activities on 22 days per week, so they meet that part of the advice.

Answer

Javier is correct. Javier reaches 300300 minutes of moderate-equivalent aerobic activity, while Stella reaches more than 7575 minutes of vigorous activity. Javier burns about 46.25%46.25\%, which is approximately 50%50\%, more calories than Stella per week.

AI analysis — may contain mistakes.

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