Answer:

Sure, let's calculate the time taken by the vehicle to cover 120 km with an average speed of 60 km/h.

We can use the formula: time = distance / speed.

For the given scenario, the distance is 120 km and the speed is 60 km/h.

So, the time taken would be: time = 120 km / 60 km/h = 2 hours.

Therefore, it would take 2 hours for the vehicle to cover a distance of 120 km with an average speed of 60 km/h.

Verified answer

Answer:

The time taken by it to cover 120 km with an average speed of 60 km/h is [tex]\bf\:\dfrac{8}{3} [/tex] hours.

Step-by-step explanation:

Given that, a vehicle runs at an average speed of 40km/h with some intervals and takes 3 hours to cover a distance of 90 km

Now, we have to find the time taken by it to cover 120 km with an average speed of 60 km/h.

Let assume that the time taken by it to cover 120 km with an average speed of 60 km/h be x hours.

Let further assume that speed of vehicle be denoted by s, distance covered by d and time taken by t.

Now, More is speed of vehicle, less is time taken.

Also, More is distance, more is time taken.

[tex]\implies\sf\:Time\:taken\:by\:vehicle \: \alpha \: Distance\:covered \times \dfrac{1}{Speed\:of\:vehicle} \\ [/tex]

[tex]\implies\sf\:t \: \alpha \: \dfrac{d}{s} \\ [/tex]

[tex]\implies\sf\:t \: = \: \dfrac{kd}{s} \\ [/tex]

where k is constant of variation.

On substituting the values, we get

[tex]\implies\sf\:3 \: = \: \dfrac{k \times 90}{40} \\ [/tex]

[tex]\implies\sf\:3 \: = \: \dfrac{k \times 9}{4} \\ [/tex]

[tex]\implies\sf\:k \: = \: \dfrac{4}{3} \\ [/tex]

Now, Consider the second case, where we have speed of vehicle is 60 km/h, distance covered is 120 km and time taken be x hours.

So, from above we have

[tex]\sf\:t \: = \: \dfrac{kd}{s} \\ [/tex]

On substituting the values, we get

[tex]\sf\:t \: = \: \dfrac{4 \times 120}{3 \times 60} \\ [/tex]

[tex]\sf\:t \: = \: \dfrac{4 \times 2}{3 \times 1} \\ [/tex]

[tex]\implies\bf\:t \: = \: \dfrac{8}{3} \: hours \\ [/tex]

Hence,

The time taken by it to cover 120 km with an average speed of 60 km/h is [tex]\bf\:\dfrac{8}{3} [/tex] hours.