if A and B ARE MOVING IN a circular track of length 0.32miles from the start line whose speed are 7 miles per hour and 9 miles per hour respectively ,then after how many seconds will they meet for the first time?

To determine when A and B will first meet on the circular track, we need to calculate the time it takes for them to have covered the same distance.

1. Convert the speeds from miles per hour to miles per second:
Speed of A = 7 miles per hour = (7/3600) miles per second
Speed of B = 9 miles per hour = (9/3600) miles per second

2. The time taken by A and B to meet can be calculated using the formula:
Time = Distance / Relative Speed

In this case, the relative speed is the difference in their speeds since they are moving in the same direction.
Relative Speed = Speed of B - Speed of A = ((9/3600) - (7/3600)) miles per second
Relative Speed = (2/3600) miles per second

3. The distance they need to cover to meet is the circumference of the circular track, which is 0.32 miles.

Time = 0.32 miles / (2/3600) miles per second

4. Convert the time to seconds:
Time = (0.32 / (2/3600)) * 3600 seconds

Time = 0.32 * 3600 / 2 seconds

Time = 576 seconds

Therefore, A and B will meet for the first time after 576 seconds.

To determine the time it takes for A and B to meet for the first time, we need to find the relative speed between the two runners. Considering their speeds are given in miles per hour, we need to convert them to miles per second for consistent units.

1 mile = 5280 feet
1 hour = 3600 seconds

So, the speed of A in miles per second is (7 miles/hour) * (1 hour/3600 seconds) = 0.00194 miles/second.
Similarly, the speed of B in miles per second is (9 miles/hour) * (1 hour/3600 seconds) = 0.0025 miles/second.

Since both A and B are moving in the same direction on the circular track, the relative speed between them is the difference between their speeds. So, the relative speed is 0.0025 miles/second - 0.00194 miles/second = 0.00056 miles/second.

To find the time it takes for A and B to meet for the first time, we can use the formula:

Time = Distance / Relative Speed

The distance they need to cover to meet for the first time is the full length of the circular track, which is 0.32 miles. Plugging in the values, we have:

Time = 0.32 miles / 0.00056 miles/second

Calculating this, we find:

Time = 571.43 seconds

So, it will take approximately 571.43 seconds for A and B to meet for the first time.