Benny runs from his home to the supermarket at an average speed of for 5 minutes and
walks to the library at an average speed of for 25 minutes. Find his average speed in th
whole journey.

Ask by Schmidt Hill. in Hong Kong

Mar 24,2025

Question

Benny runs from his home to the supermarket at an average speed of for 5 minutes and
walks to the library at an average speed of for 25 minutes. Find his average speed in th
whole journey.

Ask by Schmidt Hill. in Hong Kong

Mar 24,2025

UpStudy AI · Accepted Answer

To find Benny's average speed for the whole journey, we need to follow these steps:

1. **Calculate the distance to the supermarket**:
   - Speed = $$ 5 \, \text{m/s} $$
   - Time = $$ 5 \, \text{minutes} = 5 \times 60 \, \text{seconds} = 300 \, \text{seconds} $$
   - Distance = Speed × Time

2. **Calculate the distance to the library**:
   - Speed = $$ 2 \, \text{m/s} $$
   - Time = $$ 25 \, \text{minutes} = 25 \times 60 \, \text{seconds} = 1500 \, \text{seconds} $$
   - Distance = Speed × Time

3. **Calculate the total distance and total time**:
   - Total Distance = Distance to supermarket + Distance to library
   - Total Time = Time to supermarket + Time to library

4. **Calculate the average speed**:
   - Average Speed = Total Distance / Total Time

Let's perform the calculations step by step.

### Step 1: Distance to the supermarket
$$
d_1 = 5 \, \text{m/s} \times 300 \, \text{s}
$$

### Step 2: Distance to the library
$$
d_2 = 2 \, \text{m/s} \times 1500 \, \text{s}
$$

### Step 3: Total Distance and Total Time
$$
D = d_1 + d_2
$$
$$
T = 300 \, \text{s} + 1500 \, \text{s}
$$

### Step 4: Average Speed
$$
\text{Average Speed} = \frac{D}{T}
$$

Now, I will calculate these values.
Calculate the value by following steps:
- step0: Calculate:
  $$2\times 1500$$
- step1: Multiply the numbers:
  $$3000$$
Calculate or simplify the expression $$ 300 + 1500 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$300+1500$$
- step1: Add the numbers:
  $$1800$$
Calculate or simplify the expression $$ 5 * 300 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5\times 300$$
- step1: Multiply the numbers:
  $$1500$$
Calculate or simplify the expression $$ (1500 + 3000) / 1800 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(1500+3000\right)}{1800}$$
- step1: Remove the parentheses:
  $$\frac{1500+3000}{1800}$$
- step2: Add the numbers:
  $$\frac{4500}{1800}$$
- step3: Reduce the fraction:
  $$\frac{5}{2}$$
Now, let's summarize the calculations:

1. **Distance to the supermarket**: 
   $$
d_1 = 1500 \, \text{m}
$$

2. **Distance to the library**: 
   $$
d_2 = 3000 \, \text{m}
$$

3. **Total Distance**: 
   $$
D = 1500 + 3000 = 4500 \, \text{m}
$$

4. **Total Time**: 
   $$
T = 300 + 1500 = 1800 \, \text{s}
$$

5. **Average Speed**: 
   $$
\text{Average Speed} = \frac{4500}{1800} = 2.5 \, \text{m/s}
$$

Thus, Benny's average speed for the whole journey is $$ 2.5 \, \text{m/s} $$.
Benny's average speed for the whole journey is $$ 2.5 \, \text{m/s} $$.

Benny runs from his home to the supermarket at an average speed of for 5 minutes and
walks to the library at an average speed of for 25 minutes. Find his average speed in th
whole journey.

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Benny runs from his home to the supermarket at an average speed of for 5 minutes and walks to the library at an average speed of for 25 minutes. Find his average speed in th whole journey.

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Benny runs from his home to the supermarket at an average speed of for 5 minutes and
walks to the library at an average speed of for 25 minutes. Find his average speed in th
whole journey.