Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?

Options

A. A) 6.52
B. B) 8.14
C. C) 4.18
D. D) 5.02

Answer

To solve the problem of when the two bikers will meet while riding in opposite directions around a circular track, we can follow these steps:

### Step 1: Calculate the Circumference of the Circular Track
The diameter of the circular track is given as 40 km. To find the circumference (C) of the circular track, we can use the formula:
\[ C = \pi \times d \]
where \(d\) is the diameter. Thus:
\[ C = \pi \times 40 \text{ km} \]
Using the approximate value of \(\pi \approx 3.14\):
\[ C \approx 3.14 \times 40 = 125.6 \text{ km} \]

### Step 2: Determine the Relative Speed of the Bikers
Biker A rides at a speed of 16 km/h and Biker B rides at a speed of 14 km/h. Since they are riding in opposite directions, we can find the relative speed (R) by adding their speeds:
\[ R = 16 \text{ km/h} + 14 \text{ km/h} = 30 \text{ km/h} \]

### Step 3: Calculate the Time Taken to Meet
To find the time (T) it takes for the two bikers to meet, we can use the formula:
\[ T = \frac{\text{Total Distance}}{\text{Relative Speed}} \]
Substituting the values we have:
\[ T = \frac{125.6 \text{ km}}{30 \text{ km/h}} \]
Calculating this gives:
\[ T \approx 4.1867 \text{ hours} \]

### Step 4: Final Answer
Rounding to two decimal places, the time taken for the two bikers to meet is approximately:
\[ T \approx 4.19 \text{ hours} \]