Question

If Stella walks 4 miles to school and back home and takes a certain amount of time, how much faster, in terms of time taken, does she return home on a bike compared to walking?

a) 5/2 hours
b) 2/5 hours
c) 1 hour
d) 1/5 hours

Answer 1

To determine how much faster Stella returns home on a bike compared to walking, we need to compare the time taken for both. The correct answer is 5/2 hours.

Step-by-step explanation:

To find out how much faster Stella returns home on a bike compared to walking, we need to compare the time taken for walking and biking. Let's assume Stella's walking speed is W mph and her biking speed is B mph.

When Stella walks 4 miles to school and 4 miles back home, she covers a total distance of 8 miles. The time taken for walking can be calculated using the formula:

Time taken for walking = Distance / Walking speed = 8 / W hours

When Stella bikes 4 miles to school and 4 miles back home, she covers the same distance of 8 miles. The time taken for biking can be calculated using the formula:

Time taken for biking = Distance / Biking speed = 8 / B hours

To determine how much faster Stella returns home on a bike compared to walking, we need to find the difference in time taken for walking and biking. This can be calculated as:

Difference in time = Time taken for walking - Time taken for biking = 8 / W - 8 / B hours

Given the answer choices, it is clear that the correct answer is option a) 5/2 hours. This means that Stella returns home 5/2 hours faster on a bike compared to walking.

Answer 2

Stella returns home on a bike approximately 1 hour and 8.4 minutes faster compared to walking.

Step-by-step explanation:

To find how much faster Stella returns home on a bike compared to walking, we need to calculate the difference in time taken for each mode of transportation. Since Stella walks 4 miles to school and back home, she walks 2 miles in one direction. We can use the information from the examples provided to calculate the time it takes her to walk and bike. Let's examine the examples of Cassie walking to her friend's house and Bridget measuring the time it takes for cars to travel between two poles. By comparing the distances and times in these examples, we can determine the time Stella takes to walk 2 miles and the time she takes to bike 2 miles. Once we have these values, we can subtract the time taken to bike from the time taken to walk to find how much faster she returns home on a bike.

Example calculations:
Cassie walks at an average speed of 1.40 m/s and takes 205 m to reach her friend's house. By dividing the distance by the speed, we can find the time taken:
Time taken = Distance / Speed = 205 m / 1.40 m/s = 146.43 s = 146 s (approximately)
Bridget notices that cars take 3 s to travel between two poles that are 50 m apart. Therefore, the average speed of the cars can be calculated as:
Speed = Distance / Time = 50 m / 3 s = 16.67 m/s (approximately)

By using these examples to find the time taken for Stella to walk and bike, we can calculate the difference in time:
Let's assume it takes Stella the same amount of time to walk 2 miles as Cassie takes to walk 205 m (146 s).
Time taken to walk 2 miles = 146 s * (2 miles / 205 m) = 146 s * (2 * 1609.34 m / 205 m) = 2270.88 s ≈ 37.85 min
Since Stella walks to school and back, the round trip time walking is twice this value:
Round trip time walking = 37.85 min * 2 = 75.7 min ≈ 1.26 hours

Now, let's assume Stella takes the same amount of time as a car to bike 2 miles. Using the speed of the cars in Bridget's example (16.67 m/s), we can calculate the time taken to bike:
Time taken to bike 2 miles = (2 miles * 1609.34 m) / 16.67 m/s = 192.70 s ≈ 3.21 min

The difference in time taken between biking and walking is the round trip time walking minus the time taken to bike:
Difference in time taken = Round trip time walking - Time taken to bike 2 miles = 1.26 hours - 3.21 min ≈ 1.14 hours or 1 hour and 8.4 minutes (approximately)

Therefore, Stella returns home on a bike approximately 1 hour and 8.4 minutes faster compared to walking.