Question

You normally take a 500-mi trip, averaging 45 mi/hr. You want to increase the rate so that your travel time is at least 1hr shorter. Write an inequality that describes the situation. Solve the inequality.

Answer 1

A 500 mile trip at 45mph takes 500/45=100/9 hr=11.1 hr approx.

100/9-1=91/9 hr (10.1hr). So if the speed is reduced to v mph, v≥500/(91/9),

v≥4500/91, v≥49.45 mph (approx).

Example: if v=50 mph, time for journey is 500/50=10 hr which is less than 11.1 hr, so saving more than 1 hour on the journey.