Question

A plane left 30 min later than its scheduled time to reach its destination 1500 km away. In order to reach in time it increases its speed by 250 km/h. What is its original speed?

• A. 1000 km/h
• B. 750 km/h
• C. 600 km/h
• D. 800 km/h

Hint:

Set the scheduled time as distance/original speed, and the actual time (0.5 hour less) as distance/(original speed + 250), then solve the resulting quadratic.

Answer 1

The Correct Option is B

A faster way is to test each option against the condition: increasing the speed by 250 km/h over a 1500 km trip must save exactly 30 minutes (0.5 hour) of flying time.

1. Option A (1000 km/h): time at 1000 km/h = 1500/1000 = 1.5 h. Time at 1250 km/h = 1500/1250 = 1.2 h. Saving = 0.3 h = 18 min, not 30 min. Rejected.
2. Option B (750 km/h): time at 750 km/h = 1500/750 = 2 h. Time at 1000 km/h = 1500/1000 = 1.5 h. Saving = 0.5 h = 30 min. This matches exactly.
3. Option C (600 km/h): time at 600 km/h = 1500/600 = 2.5 h. Time at 850 km/h = 1500/850 $\approx$ 1.76 h. Saving $\approx$ 0.74 h $\approx$ 44 min, too much. Rejected.
4. Option D (800 km/h): time at 800 km/h = 1500/800 = 1.875 h. Time at 1050 km/h = 1500/1050 $\approx$ 1.43 h. Saving $\approx$ 0.45 h $\approx$ 27 min, close but not exactly 30 min. Rejected.

Only the original speed of 750 km/h produces exactly a 30 minute saving, confirming \( v = 750 \) km/h as the answer.