It takes Julia 40 minutes to drive to work at an average speed of 60 km/h. a) Julia drives at an average speed of 120 km/h. How long will it take Julia to drive to work? b) It take... It takes Julia 40 minutes to drive to work at an average speed of 60 km/h. a) Julia drives at an average speed of 120 km/h. How long will it take Julia to drive to work? b) It takes Julia 80 minutes to drive to work. What is Julia's average speed? Read more

Steps to Solve

1. Calculate Distance for Part a

To find the distance that Julia travels to work, we can use the formula:

$$ \text{Distance} = \text{Speed} \times \text{Time} $$

First, we convert the time taken from minutes to hours for consistency in units. Julia takes 40 minutes, which is:

$$ \text{Time in hours} = \frac{40}{60} = \frac{2}{3} \text{ hours} $$

Now we can find the distance:

$$ \text{Distance} = 60 , \text{km/h} \times \frac{2}{3} , \text{h} = 40 , \text{km} $$

2. Calculate Time for Part a at 120 km/h

Now we find the time it takes Julia to drive to work at 120 km/h using the distance calculated:

$$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{40 , \text{km}}{120 , \text{km/h}} = \frac{1}{3} , \text{h} $$

Convert hours back to minutes:

$$ \text{Time in minutes} = \frac{1}{3} \times 60 = 20 , \text{minutes} $$

3. Find Average Speed for Part b

For part b, we need to find Julia's average speed based on a time of 80 minutes. First, we convert 80 minutes to hours:

$$ \text{Time in hours} = \frac{80}{60} = \frac{4}{3} , \text{hours} $$

Using the same distance (40 km), we can find her average speed:

$$ \text{Average Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{40 , \text{km}}{\frac{4}{3} , \text{h}} = 40 , \text{km} \times \frac{3}{4} = 30 , \text{km/h} $$