Alan went from San Francisco to Los Angeles ,about 400 miles,averaging (x+5)mph.On his journey from Los Angeles to Redding,about 500 miles,the average (x-5)mph.Then he returned to San Francisco,about 200 miles,averaging (x^2-25)mph.How long did it take him,in terms of x,to make the round trip?

distance = rate times time.

Use the formula and plug in the constants and variables.

To find out how long it took Alan to make the round trip, we need to calculate the time it took for each leg of the journey and then add them together.

Let's start by finding the time it took for Alan to travel from San Francisco to Los Angeles, which is a distance of 400 miles at an average speed of (x+5) mph. The time can be calculated using the formula: time = distance / speed.

So, the time taken for the first leg of the journey is:
Time1 = 400 miles / (x+5) mph

Next, let's find the time it took for Alan to travel from Los Angeles to Redding, which is a distance of 500 miles at an average speed of (x-5) mph.
Time2 = 500 miles / (x-5) mph

Finally, let's calculate the time it took for Alan to return from Redding to San Francisco, which is a distance of 200 miles at an average speed of (x^2-25) mph.
Time3 = 200 miles / (x^2-25) mph

Now, to find the total time for the round trip, we add the times together:
Total time = Time1 + Time2 + Time3

Therefore, the total time taken by Alan to make the round trip, in terms of x, is:
Total time = (400 / (x+5)) + (500 / (x-5)) + (200 / (x^2-25))