Challenge Andy​, Beth​, and Cathy each went for a walk yesterday afternoon. Andy walked 2 and three fourths mi

Question

at a constant speed of 2 and one half mi divided by h
. Beth walked 1 and three fourths mi
at a constant speed of 1 and one fourth mi divided by h
. Cathy walked for 1 h and 13 min at a constant speed of 2 and one half mi divided by h
. List the three people in order of the times they spent walking from least time to greatest time.
Question content area bottom
Part 1
Choose the correct answer below.
A.
Beth​, Andy​, Cathy
B.
Beth​, Cathy​, Andy
C.
Andy​, Beth​, Cathy
D.
Andy​, Cathy​, Beth
E.
Cathy​, Beth​, Andy
F.
Cathy​, Andy​, Beth

Answer 1

To determine the time each person spent walking, we can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Let's calculate the time for each person.

Andy:

• Distance = \(2 \frac{3}{4}\) miles = \(2.75\) miles
• Speed = \(2 \frac{1}{2}\) miles per hour = \(2.5\) miles per hour

\[ \text{Time}_A = \frac{2.75 \text{ miles}}{2.5 \text{ miles/hour}} = 1.1 \text{ hours} \]

Beth:

• Distance = \(1 \frac{3}{4}\) miles = \(1.75\) miles
• Speed = \(1 \frac{1}{4}\) miles per hour = \(1.25\) miles per hour

\[ \text{Time}_B = \frac{1.75 \text{ miles}}{1.25 \text{ miles/hour}} = 1.4 \text{ hours} \]

Cathy:

• Time = \(1\) hour and \(13\) minutes = \(1 + \frac{13}{60}\) hours = \(\frac{73}{60}\) hours
• Speed = \(2 \frac{1}{2}\) miles per hour = \(2.5\) miles per hour

Since we already have the time Cathy walked, we can convert this to a decimal for easier comparison:

\[ 1 + \frac{13}{60} \approx 1.2167 \text{ hours} \]

Now, we compare the times:

• Andy: \(1.1 \text{ hours}\)
• Beth: \(1.4 \text{ hours}\)
• Cathy: \(\approx 1.2167 \text{ hours}\)

Now, ordering the times from least to greatest:

1. Andy: \(1.1\) hours
2. Cathy: \(1.2167\) hours
3. Beth: \(1.4\) hours

So the final order of times spent walking from least to greatest is:

A. Andy, Cathy, Beth

Thus, the answer is:

C. Andy, Cathy, Beth