James drove the 24 miles to two and back in hour. On the return trip, he was able to average 20 miles per hour faster than he averaged on the trip to town. what was his average speed on the trip to town?

v= speed to town

time going=24/v
time coming=24/(v+20)
time going+timecoming=1hr

1=24/v + 24/(v+20)
v(v+20)=24(v+20)+24v
v^2+20v-48v-480=0
v^2-28v-480=0

v=(28+-sqrt(28^2+1920))/2
v=40

To find James' average speed on the trip to town, we can set up a system of equations based on the given information.

Let's assume that James' average speed on the trip to town is represented by "x" miles per hour.

Given that the total distance traveled is 24 miles, we can use the formula Speed = Distance / Time. Hence, the time taken to travel to town is 24 / x hours.

On the return trip, James was able to average 20 miles per hour faster, so his average speed would be x + 20 miles per hour. The time taken to travel back is 24 / (x + 20) hours.

The total time for the round trip is 1 hour. Therefore, the sum of the time taken to travel to town and the time taken to travel back should be equal to 1:

24 / x + 24 / (x + 20) = 1

Now, we can solve this equation to find the value of x, which represents James' average speed on the trip to town.

To solve the equation, we can multiply every term by the common denominator, which is x(x + 20):

24(x + 20) + 24x = x(x + 20)

Simplifying the equation gives:

24x + 480 + 24x = x^2 + 20x

48x + 480 = x^2 + 20x

Rearranging and simplifying further gives:

x^2 - 28x - 480 = 0

Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula.

After solving the equation, you will find two possible values for x. Since we're looking for the average speed on the trip to town, choose the positive value that makes sense in the context of the problem.