When traveling b/w two towns the time taken varies inversely with the average speed when average is 42km/hour the journey takes 2hours20minute

Physics

To find the time taken for the journey when the average speed is different, we can use the concept of inverse variation.

Inverse variation means that two quantities are inversely proportional to each other. In this case, the time taken and the average speed are inversely proportional.

Let's denote the time taken as T (in hours) and the average speed as S (in km/h). We can write the inverse variation equation as:

T = k/S

Here, k is a constant of variation that we need to determine.

We are given that when the average speed is 42 km/h, the journey takes 2 hours and 20 minutes. We need to convert the time to hours, so 20 minutes is equal to 20/60 = 1/3 hour.

Substituting these values into the equation:

2 + 1/3 = k/42

To solve for k, we can cross-multiply:

k = (2 + 1/3) * 42

k = (7/3) * 42

k = 98

Now we have our constant of variation k. We can use this value to find the time taken for any average speed.

For example, if we want to find the time taken when the average speed is 60 km/h:

T = 98/60

T ≈ 1.63 hours

So, the journey would take approximately 1 hour and 38 minutes when the average speed is 60 km/h.