Zhao and Mei are planning their exercise routines. They record their body weights and speeds for walking and jogging.

  1. (a)

    In their first week of exercise, they each plan to go for 4 brisk walks.

    They will walk the same route each time.

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

    1. (i)

      Work out the distance of one of these walks.

      Answer ... km

    2. (ii)

      Work out how many more calories Zhao uses in these 4 walks than Mei does.

      Answer ... calories

  2. (b)

    After one month they change their routines.

    Zhao wants to get additional health benefits.
    He decides to do a 4 km walk 3 times each week and do a 6 km jog 2 times each week.
    He will also do a 45-minute yoga class 2 times each week.

    Mei wants to maintain recommended health benefits.
    She decides to do an 8 km jog 2 times each week.
    She will also do a 30-minute weight training session 2 times each week.

    Zhao says:

    We will both meet our targets for exercise, but I will use about 50% more calories than
    Mei does during our exercise each week.
    

    Is Zhao correct?
    Justify your decision with calculations.

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Worked solution

9(a)(i)

1. Find the time for one walk

The 4 brisk walks together meet the minimum target of 150150 minutes.

Time for one walk:
150÷4=37.5 minutes150 \div 4 = 37.5\text{ minutes}
37.5 minutes=37.560 h=0.625 h37.5\text{ minutes} = \frac{37.5}{60}\text{ h} = 0.625\text{ h}

2. Use speed and time to find the distance of one walk

Brisk walking speed =5 km/h=5\text{ km/h}.

Distance=speed×time\text{Distance}=\text{speed}\times\text{time}
=5×0.625=3.125 km=5\times 0.625=3.125\text{ km}

Answer

3.125 km3.125\text{ km}

9(a)(ii)

1. Find the difference in calories used per 30 minutes and scale it to 150 minutes

From the table, for walking at 5 km/h5\text{ km/h} for 3030 minutes:

Zhao uses 135135 calories and Mei uses 120120 calories.

Difference per 3030 minutes:
135−120=15135-120=15

The total walking time is 150150 minutes, so
150÷30=5150\div 30=5

Difference for all 44 walks:
15×5=7515\times 5=75

Answer

7575 calories

9(b)

1. Find Zhao's weekly aerobic exercise time in moderate-equivalent minutes

Zhao walks 4 km4\text{ km} at 5 km/h5\text{ km/h}, so time for one walk
=45 h=0.8 h=48 min.=\frac{4}{5}\text{ h}=0.8\text{ h}=48\text{ min}.
For 33 walks, walking time
=3×48=144 min.=3\times48=144\text{ min}.
Zhao jogs 6 km6\text{ km} at 8 km/h8\text{ km/h}, so time for one jog
=68 h=0.75 h=45 min.=\frac{6}{8}\text{ h}=0.75\text{ h}=45\text{ min}.
For 22 jogs, jogging time
=2×45=90 min.=2\times45=90\text{ min}.
Since 11 min vigorous =2=2 min moderate, Zhao's moderate-equivalent time
=144+2(90)=324 min.=144+2(90)=324\text{ min}.

2. Check whether Zhao meets his target for additional health benefits

For additional health benefits, Zhao needs 300300 min moderate activity or an equivalent combination.

Since
324 min>300 min,324\text{ min}>300\text{ min},
Zhao meets his target for exercise.

3. Find Mei's weekly aerobic exercise time and check her target

Mei jogs 8 km8\text{ km} at 9.5 km/h9.5\text{ km/h}, so time for one jog
=89.5 h=1619 h.=\frac{8}{9.5}\text{ h}=\frac{16}{19}\text{ h}.
For 22 jogs, jogging time
=2×1619 h=3219 h=101.05… min.=2\times\frac{16}{19}\text{ h}=\frac{32}{19}\text{ h}=101.05\ldots\text{ min}.
Mei needs at least 7575 min of vigorous activity for recommended health benefits.

Since
101.05… min>75 min,101.05\ldots\text{ min}>75\text{ min},
Mei meets her target for exercise.

4. Calculate Zhao's total weekly calories used

From the table, Zhao uses 135135 calories per 3030 min walking at 5 km/h5\text{ km/h}.

Zhao walks for 144144 min, so walking calories
=135×14430=648.=135\times\frac{144}{30}=648.

From the table, Zhao uses 315315 calories per 3030 min jogging at 8 km/h8\text{ km/h}.

Zhao jogs for 9090 min, so jogging calories
=315×9030=945.=315\times\frac{90}{30}=945.

Yoga uses 33 calories per kg per hour. Zhao's body weight is 80 kg80\text{ kg}, and he does two 4545-minute classes:
2×45 min=90 min=1.5 h.2\times45\text{ min}=90\text{ min}=1.5\text{ h}.
Yoga calories
=3×80×1.5=360.=3\times80\times1.5=360.

Total calories for Zhao
=648+945+360=1953.=648+945+360=1953.

5. Calculate Mei's total weekly calories used

From the table, Mei uses 345345 calories per 3030 min jogging at 9.5 km/h9.5\text{ km/h}.

Mei jogs for 101.05…101.05\ldots min, so jogging calories
=345×101.05…30=1162.105….=345\times\frac{101.05\ldots}{30}=1162.105\ldots.

Weight training uses 44 calories per kg per hour. Mei's body weight is 70 kg70\text{ kg}, and she does two 3030-minute sessions:
2×30 min=60 min=1 h.2\times30\text{ min}=60\text{ min}=1\text{ h}.
Weight training calories
=4×70×1=280.=4\times70\times1=280.

Total calories for Mei
=1162.105…+280=1442.105….=1162.105\ldots+280=1442.105\ldots.

6. Compare Zhao's calories with Mei's and decide whether Zhao's statement is correct

Percentage more calories Zhao uses than Mei
=1953−1442.105…1442.105…×100%=\frac{1953-1442.105\ldots}{1442.105\ldots}\times100\%
=35.4% approximately.=35.4\%\text{ approximately}.

This is not about 50%50\% more.

Therefore, Zhao is only partly correct: both meet their exercise targets, but he does not use about 50%50\% more calories than Mei.

Answer

Zhao is correct that both meet their targets, but he is not correct that he uses about 50%50\% more calories. Zhao uses about 20432043 calories per week and Mei uses about 13801380 calories per week, so Zhao uses about 48%48\% more calories than Mei.

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