Wade is making a tile mosaic . He begins the project by laying tile at a speed of 50 pieces per hour for 3.5 hours . He is then interrupted from his work for 60 minutes . He resume working and lays tile at a speed of 35 pieces per hours until he has laid 280 pieces of tile total. How many hours did Wade spend working on the mosaic after he started working again ?

Options

A. `2.5`
B. `3`
C. `3.5`
D. `4`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the number of tiles laid in the first period
Wade lays tiles at a speed of 50 pieces per hour for 3.5 hours.

\[ \text{Total tiles laid in the first period} = \text{Speed} \times \text{Time} = 50 \, \text{pieces/hour} \times 3.5 \, \text{hours} \]

Calculating this gives:

\[ 50 \times 3.5 = 175 \, \text{pieces} \]

### Step 2: Determine the total number of tiles laid
The problem states that Wade laid a total of 280 pieces of tile.

### Step 3: Calculate the number of tiles laid in the second period
To find out how many tiles were laid in the second period, we subtract the tiles laid in the first period from the total:

\[ \text{Tiles laid in the second period} = \text{Total tiles} - \text{Tiles laid in the first period} = 280 - 175 \]

Calculating this gives:

\[ 280 - 175 = 105 \, \text{pieces} \]

### Step 4: Calculate the time taken in the second period
Wade resumes working at a speed of 35 pieces per hour. We can find the time taken to lay the remaining 105 pieces using the formula:

\[ \text{Time} = \frac{\text{Total pieces}}{\text{Speed}} = \frac{105 \, \text{pieces}}{35 \, \text{pieces/hour}} \]

Calculating this gives:

\[ \frac{105}{35} = 3 \, \text{hours} \]

### Conclusion
Wade spent **3 hours** working on the mosaic after he started working again.

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