Two rockets approach each other, one at 42000 mph and the other at 18000 mph. They start 3256 miles apart. How far are they apart (in miles) 1 minute before impact ?

Options

A. 1628
B. 1000
C. 826
D. 1200

Answer

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

### Step 1: Determine the speeds of the rockets
The speeds of the two rockets are given as:
- Rocket 1: 42,000 mph
- Rocket 2: 18,000 mph

### Step 2: Calculate the relative speed
To find out how fast the two rockets are approaching each other, we need to add their speeds together:
\[ \text{Relative Speed} = \text{Speed of Rocket 1} + \text{Speed of Rocket 2} \]
\[ \text{Relative Speed} = 42,000 \text{ mph} + 18,000 \text{ mph} = 60,000 \text{ mph} \]

### Step 3: Calculate the distance covered in 1 minute
Since the relative speed is in miles per hour, we need to convert it to miles per minute. There are 60 minutes in an hour, so:
\[ \text{Distance covered in 1 minute} = \frac{\text{Relative Speed}}{60} \]
\[ \text{Distance covered in 1 minute} = \frac{60,000 \text{ miles per hour}}{60} = 1,000 \text{ miles} \]

### Step 4: Determine the distance apart 1 minute before impact
Since the rockets are approaching each other and will cover 1,000 miles in the last minute before they collide, we need to find out how far apart they are just before that minute:
\[ \text{Distance apart 1 minute before impact} = \text{Distance at the start} - \text{Distance covered in 1 minute} \]
\[ \text{Distance apart 1 minute before impact} = 3,256 \text{ miles} - 1,000 \text{ miles} = 2,256 \text{ miles} \]

### Final Answer
The distance between the two rockets 1 minute before impact is **2,256 miles**.

---