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A fun walk is 8 km long. Junice has walked 3 km and Dineo has walked 4 km. a) How far must Junice walk to finish? b) What fraction of the fun walk did Junice complete? c) How long will it take Junice

Mathematics

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Answers

6 parts
a

5 km\text{5 km}

b

38\frac{3}{8}

c

2 hours and 40 minutes\text{2 hours and 40 minutes}

d

4 km\text{4 km}

e

12\frac{1}{2}

f

2 hours\text{2 hours}

Step-by-step solution

9 steps

The total length of the fun walk is 8 km8 \text{ km}.
Junice covered 3 km3 \text{ km} in one hour.
Dineo covered 4 km4 \text{ km} in one hour.

Part a· 1 step

How far must Junice walk to finish the fun walk?

  1. Subtract the distance Junice has already walked from the total distance.

    8 km−3 km=5 km8 \text{ km} - 3 \text{ km} = 5 \text{ km}

    Junice must walk 5 km\boxed{\text{5 km}} to finish the fun walk.

Part b

38\frac{3}{8}

What fraction of the whole fun walk did Junice complete after one hour?

  1. Form a fraction with the distance Junice walked as the numerator and the total distance as the denominator.

    3 km8 km=38\frac{3 \text{ km}}{8 \text{ km}} = \frac{3}{8}

    Junice completed 38\boxed{\frac{3}{8}} of the fun walk.

Part c

2 hours and 40 minutes\text{2 hours and 40 minutes}

If Junice walks at the same pace, how long will it take her to finish the race?

  1. Calculate Junice's pace.

    Pace=DistanceTime=3 km1 hour\text{Pace} = \frac{\text{Distance}}{\text{Time}} = \frac{3 \text{ km}}{1 \text{ hour}}
  2. Calculate the total time needed to complete the 8 km8 \text{ km} walk at this pace.

    Time=Total DistancePace=8 km3 km/hour=83 hours\text{Time} = \frac{\text{Total Distance}}{\text{Pace}} = \frac{8 \text{ km}}{3 \text{ km/hour}} = \frac{8}{3} \text{ hours}
  3. Convert the fraction of an hour to minutes.

    83 hours=223 hours=2 hours+(23×60) minutes=2 hours and 40 minutes\frac{8}{3} \text{ hours} = 2 \frac{2}{3} \text{ hours} = 2 \text{ hours} + \left(\frac{2}{3} \times 60\right) \text{ minutes} = 2 \text{ hours and } 40 \text{ minutes}

    It will take Junice 2 hours and 40 minutes\boxed{\text{2 hours and 40 minutes}} to finish the race.

Part d

4 km\text{4 km}

How far must Dineo walk to finish the fun walk?

  1. Subtract the distance Dineo has already walked from the total distance.

    8 km−4 km=4 km8 \text{ km} - 4 \text{ km} = 4 \text{ km}

    Dineo must walk 4 km\boxed{\text{4 km}} to finish the fun walk.

Part e

12\frac{1}{2}

What fraction of the whole fun walk did Dineo complete after one hour?

  1. Form a fraction with the distance Dineo walked as the numerator and the total distance as the denominator.

    4 km8 km=12\frac{4 \text{ km}}{8 \text{ km}} = \frac{1}{2}

    Dineo completed 12\boxed{\frac{1}{2}} of the fun walk.

Part f

2 hours\text{2 hours}

If Dineo walks at the same pace how long will it take him to finish the race?

  1. Calculate Dineo's pace.

    Pace=DistanceTime=4 km1 hour\text{Pace} = \frac{\text{Distance}}{\text{Time}} = \frac{4 \text{ km}}{1 \text{ hour}}
  2. Calculate the total time needed to complete the 8 km8 \text{ km} walk at this pace.

    Time=Total DistancePace=8 km4 km/hour=2 hours\text{Time} = \frac{\text{Total Distance}}{\text{Pace}} = \frac{8 \text{ km}}{4 \text{ km/hour}} = 2 \text{ hours}

    It will take Dineo 2 hours\boxed{\text{2 hours}} to finish the race.

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