Let's use the information given to calculate Akhil's usual speed first.

We know that Akhil takes 30 minutes (0.5 hours) extra to cover a distance of 150 km when he drives 10 km/h slower than his usual speed.

Let "S" be Akhil's usual speed in km/h. So, his slower speed would be (S - 10) km/h.

The time taken to cover a distance is equal to the distance divided by the speed: Time = Distance / Speed

At his usual speed, it takes him: Time at usual speed = 150 km / S hours

At the slower speed, it takes him: Time at slower speed = 150 km / (S - 10) hours

The difference in time between these two scenarios is 0.5 hours (30 minutes): Time at slower speed - Time at usual speed = 0.5 hours

Now, we can set up the equation and solve for S:

(150 km / (S - 10)) - (150 km / S) = 0.5

To solve this equation, we'll first get a common denominator: [150S - 150(S - 10)] / [S(S - 10)] = 0.5

Now, simplify and solve for S: [150S - 150S + 1500] / [S(S - 10)] = 0.5

1500 / [S(S - 10)] = 0.5

Now, cross-multiply: 2 * 1500 = S(S - 10)

3000 = S^2 - 10S

S^2 - 10S - 3000 = 0

Now, we can solve this quadratic equation for S using the quadratic formula:

S = [-(-10) ± √((-10)^2 - 4(1)(-3000))] / (2(1))

S = [10 ± √(100 + 12000)] / 2

S = [10 ± √12100] / 2

S = [10 ± 110] / 2

Now, we have two possible values for S, but we'll take the positive one because speed cannot be negative:

S = (10 + 110) / 2 = 120/2 = 60 km/h

So, Akhil's usual speed is 60 km/h.

Now, we want to find out how much time he will take to drive 90 km when he drives 15 km/h slower than his usual speed, which would be (60 - 15) = 45 km/h.

Time = Distance / Speed Time = 90 km / 45 km/h = 2 hours

Akhil will take 2 hours to drive 90 km when he drives 15 km/h slower than his usual speed.