Question

Seetha drove to work at 30 miles per hour. How fast would she need to drive home for the average speed for her round trip commute to be 60 miles per hour?

Answer 1

Let's assume the distance from Seetha's home to work is x miles.

To find the average speed for her round trip commute, we need to find the total distance traveled.

Since she drives at 30 miles per hour from home to work, the time taken from home to work is given by: time = distance/speed = x/30.

Similarly, the time taken from work to home can be calculated as: time = distance/speed = x/speed (let's assume this speed as v miles per hour).

The total distance traveled is 2x (since it's a round trip).

The total time taken is x/30 + x/v.

We are given that the average speed for her round trip commute is 60 miles per hour.

Average speed = total distance/total time = 2x / (x/30 + x/v).

But the average speed is given as 60 miles per hour.

So, we get the equation: 60 = 2x / (x/30 + x/v).

Let's divide both sides of the equation by 2x to simplify it: 60 / (2x) = 1 / (x/30 + x/v).

Now, let's take the reciprocal of both sides to further simplify: (2x) / 60 = x/30 + x/v.

Dividing both sides by x gives: (2/60) = (1/30) + (1/v).

Simplifying it further, 1/30 = 1/v.

Rearranging this equation gives: v = 30.

So, she would need to drive at 30 miles per hour to have an average speed of 60 miles per hour for her round trip commute.