If the speed were increased by 30 mph, a 100-mile trip would take 3 hours less time.How long will the trip take at the slower speed?
A) 5 hours
B) 100 hours
C) 20 hours
D) 3 hours
E) 23 hours

Question

If the speed were increased by 30 mph, a 100-mile trip would take 3 hours less time.How long will the trip take at the slower speed? 
A) 5 hours
B) 100 hours
C) 20 hours
D) 3 hours
E) 23 hours

Quizplus · Accepted Answer

At the original speed, let's denote the time taken to complete the trip as $T$ hours and the original speed as $S$ mph. The distance of the trip is given as 100 miles. Therefore, we can write the equation $S \times T = 100$. If the speed is increased by 30 mph, the new speed becomes $S + 30$ mph, and the time taken for the trip becomes $T - 3$ hours. We can write another equation for the trip with the increased speed: $(S + 30) \times (T - 3) = 100$. Solving these two equations simultaneously, we find that $T = 5$ hours. This means the trip will take 5 hours at the slower speed.

If the Speed Were Increased by 30 Mph, a 100-Mile