Multiple choice

A plane left 30 minutes later than its scheduled time. If it had to increase its usual speed by 250 km/hr in order to reach the destination 1500 km away on time, then which of the following options is true?

  1. Usual speed of the plane was 850 km/hr.

  2. Increased speed of the plane was 1000 km/hr.

  3. The plane will cover 750 km in 1.5 hours on travelling with usual speed.

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be usual speed. 1500/v - 1500/(v+250) = 0.5. 3000(v+250) - 3000v = v(v+250). 750000 = v^2 + 250v. v^2 + 250v - 750000 = 0. (v+1000)(v-750) = 0. v = 750. Increased speed = 1000.

AI explanation

The plane needs to make up for 30 minutes, which is 0.5 hours, so the equation is (1500 divided by usual speed) minus (1500 divided by (usual speed + 250)) equals 0.5. Solving this quadratic equation yields a usual speed of 750 km/hr, which means the increased speed is 750 plus 250, equaling 1000 km/hr. Because the other numerical statements fail to match this speed, the true statement is that the increased speed of the plane was 1000 km/hr.

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