a man was arrested for exeeding the speed limit by 10 miles an hour. a second man was charged with exceeding the same limit by twice as much. the second man was driving 35 miles per hour then what was the speed limit.

To solve this problem, we need to break it down step by step. We know that the second man was charged with exceeding the speed limit by twice as much as the first man. Let's denote the speed limit as "S" miles per hour. The first man exceeded the speed limit by 10 miles per hour, which means he was driving at a speed of S + 10 mph. The second man, on the other hand, exceeded the speed limit by twice that amount, which is 20 miles per hour. Since we know the second man was driving at 35 mph, we can set up an equation to find the speed limit.

Setting Up the Equation

From the information given, we can express the speed of the second man in terms of the speed limit:

• Speed of the second man = Speed limit + 20 mph
• We know the speed of the second man = 35 mph

Now we can write the equation:

S + 20 = 35

Solving for the Speed Limit

To find the speed limit, we simply need to isolate S in the equation:

• Subtract 20 from both sides:
• S = 35 - 20
• S = 15

Conclusion

Therefore, the speed limit is 15 miles per hour. This means the first man was driving at 25 mph (15 + 10), and the second man was indeed driving at 35 mph, which is 20 mph over the speed limit. This example illustrates how we can use basic algebra to solve real-world problems involving speed and limits.