On a family vacation with his RV, Bill drove a total of x

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On a family vacation with his RV, Bill drove a total of \(x\) miles. He averaged 50 miles per hour for the entire trip except for a 10-mile section when he averaged only 20 miles per hour because of construction. His travel time for the \(x-\)mile trip was what percent greater than it would have been if he had been able to travel 50 miles per hour for the entire trip?

A. \(1.5\)%

B. \(15\)%

C. \(\frac{50}{x}\)%

D. \(\frac{300}{x}\)%

E. \(\frac{1500}{x}\)%

OA E

If Bill had traveled 50 mph for the entire trip, his time would have been x/50 hours. Since there was a 10-mile section where he had to travel 20 mph, his time for this section was 10/20 = 1/2 hour, and his time for the remaining (x - 10) miles was (x - 10)/50 = x/50 - 1/5 hours. Thus, his actual total time for the x-mile trip was 1/2 + x/50 - 1/5 = x/50 + 3/10 hours. We can determine the percent greater that this actual time is than what the time would have been if he had been able to travel 50 mph for the entire trip as: was:

[(x/50 + 3/10 - x/50)/(x/50)] * 100

[(3/10)/(x/50)] * 100

[150/(10x)] * 100

(15/x) *100

1500/x

Thus, the actual time was 1500/x percent greater than the time that he would have needed had he been able to travel 50 mph for the entire trip.

Answer: E