A and B stand at distinct points of a circular race track of length 135 m. They cycle at a speed of a m/s and b m/s. They meet for the first time 5 secs after they start the race.

A and B stand at distinct points of a circular race track of length 135 m. They cycle at a speed of a m/s and b m/s. They meet for the first time 5 secs after they start the race and for the second time 14 seconds from the time they start the race. Now if B had started in the opposite direction to the one he had originally started. They would have met for the first time after 60 seconds. If B is quicker then A, then find b?

b = 8 m/s.

Here's how

First Meeting after 5 seconds: When they meet for the first time after 5 seconds, the total distance covered by A and B combined is equal to the circumference of the circular track, which is 135 meters.

So, we have the equation:

"5a + 5b = 135" [since distance = speed × time]

Second Meeting after 14 seconds: When they meet for the second time after 14 seconds, A has covered one lap more than B. The difference in the distances covered by A and B in 14 seconds would be one lap.

So, we have the equation:

"14a - 14b = 135" [same logic as above]

Meeting after 60 seconds in opposite directions:

When they meet for the first time after 60 seconds while moving in opposite directions, the relative speed is the sum of their individual speeds.

So, we have the equation:

"60(a+b) = 135"

Now, we can solve these equations to find the value of 'b'.

From equation (1):

"5a + 5b = 135"

"a + b = 27"

From equation (2):

"14a - 14b = 135"

"a - b = 135/14"

Now, solving these two equations simultaneously:

"a + b = 27"

"a - b = 135/14"

Adding the two equations, we get:

"2a = 27 + 135/14"

"2a = (378 + 135)/14"

"2a = 513/14"

"a = 513/28"

Now, substituting the value of 'a' into equation (1):

"(513/28) + b = 27"

"b = 27 - (513/28)"

"b = (756 - 513)/28"

"b = 243/28"

Thus, "b = 243/28 ≈ 8.68" meters per second.

Time, Distance and Speed

Time, distance, and speed are interconnected concepts in physics and mathematics that are fundamental to understanding motion and travel. Here's a brief overview of each:

1. Time: Time is a measure of the duration between events. It's often denoted in units such as seconds, minutes, hours, days, etc. Time is a continuous and unidirectional dimension that flows uniformly forward (according to conventional understanding).

2. Distance: Distance is a measure of the length between two points. It can be measured in various units such as meters, kilometers, miles, etc. Distance is also a continuous dimension but is not inherently directional; it simply describes the extent of space between two objects or points.

3. Speed: Speed is a measure of how quickly an object moves through space. It's typically measured in distance units per unit of time, such as meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), etc. Speed indicates the rate of change of distance with respect to time.

These concepts are related by the following formula:

Speed = Distance / Time

This formula can be rearranged to solve for any of the three variables if the other two are known.

• If you know the speed and the time, you can find the distance traveled using the formula: Distance = Speed * Time
• If you know the distance and the time, you can find the speed using the formula: Speed = Distance / Time
• If you know the distance and the speed, you can find the time using the formula: Time = Distance / Speed

Understanding these concepts and relationships is crucial for solving problems involving motion, such as calculating travel times, determining vehicle velocities, or estimating arrival times.