Answer :
We begin by finding the distance Julia drives to work using her initial information.
1. Since Julia drives at an average speed of [tex]$60\text{ km/h}$[/tex] and it takes her [tex]$40$[/tex] minutes to reach work, we first convert the time into hours:
[tex]$$
40 \text{ minutes} = \frac{40}{60} = \frac{2}{3} \text{ hours}.
$$[/tex]
2. The distance to work can then be calculated using the formula:
[tex]$$
\text{Distance} = \text{Speed} \times \text{Time} = 60 \times \frac{2}{3} = 40 \text{ km}.
$$[/tex]
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Part (a):
Julia now drives at an average speed of [tex]$120\text{ km/h}$[/tex]. We need to determine how long it takes her to cover the same [tex]$40\text{ km}$[/tex].
1. The time taken is given by:
[tex]$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{40}{120} = \frac{1}{3} \text{ hours}.
$$[/tex]
2. To express this time in minutes, we convert hours to minutes:
[tex]$$
\frac{1}{3} \text{ hours} \times 60 \text{ minutes/hour} = 20 \text{ minutes}.
$$[/tex]
Thus, at [tex]$120\text{ km/h}$[/tex], it will take Julia [tex]$20$[/tex] minutes to drive to work.
---
Part (b):
Now, suppose it takes Julia [tex]$80$[/tex] minutes to cover the same distance. We need to find her average speed in this case.
1. First, convert [tex]$80$[/tex] minutes to hours:
[tex]$$
80 \text{ minutes} = \frac{80}{60} = \frac{4}{3} \text{ hours}.
$$[/tex]
2. The average speed is then calculated by:
[tex]$$
\text{Average Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{40}{\frac{4}{3}} = 40 \times \frac{3}{4} = 30 \text{ km/h}.
$$[/tex]
---
Summary:
- When Julia drives at [tex]$120\text{ km/h}$[/tex], it takes her [tex]$20$[/tex] minutes to drive to work.
- When it takes her [tex]$80$[/tex] minutes to drive to work, her average speed is [tex]$30\text{ km/h}$[/tex].
1. Since Julia drives at an average speed of [tex]$60\text{ km/h}$[/tex] and it takes her [tex]$40$[/tex] minutes to reach work, we first convert the time into hours:
[tex]$$
40 \text{ minutes} = \frac{40}{60} = \frac{2}{3} \text{ hours}.
$$[/tex]
2. The distance to work can then be calculated using the formula:
[tex]$$
\text{Distance} = \text{Speed} \times \text{Time} = 60 \times \frac{2}{3} = 40 \text{ km}.
$$[/tex]
---
Part (a):
Julia now drives at an average speed of [tex]$120\text{ km/h}$[/tex]. We need to determine how long it takes her to cover the same [tex]$40\text{ km}$[/tex].
1. The time taken is given by:
[tex]$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{40}{120} = \frac{1}{3} \text{ hours}.
$$[/tex]
2. To express this time in minutes, we convert hours to minutes:
[tex]$$
\frac{1}{3} \text{ hours} \times 60 \text{ minutes/hour} = 20 \text{ minutes}.
$$[/tex]
Thus, at [tex]$120\text{ km/h}$[/tex], it will take Julia [tex]$20$[/tex] minutes to drive to work.
---
Part (b):
Now, suppose it takes Julia [tex]$80$[/tex] minutes to cover the same distance. We need to find her average speed in this case.
1. First, convert [tex]$80$[/tex] minutes to hours:
[tex]$$
80 \text{ minutes} = \frac{80}{60} = \frac{4}{3} \text{ hours}.
$$[/tex]
2. The average speed is then calculated by:
[tex]$$
\text{Average Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{40}{\frac{4}{3}} = 40 \times \frac{3}{4} = 30 \text{ km/h}.
$$[/tex]
---
Summary:
- When Julia drives at [tex]$120\text{ km/h}$[/tex], it takes her [tex]$20$[/tex] minutes to drive to work.
- When it takes her [tex]$80$[/tex] minutes to drive to work, her average speed is [tex]$30\text{ km/h}$[/tex].
