Multiple choice

A plane left $40$ minutes late due to bad weather and in order to reach its destination, $1600$ km away in time, it had to increase its speed by $400$km/hr from its usual speed. Find the usual speed of the plane.

  1. $1000\text{km/h}$
  2. $1600\text{km/h}$
  3. $800\text{km/h}$
  4. $600\text{km/h}$
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C Correct answer
Explanation

Let v be the usual speed. Time taken at usual speed is 1600/v, and at increased speed is 1600/(v+400). The difference is 40 minutes (2/3 hours). Solving 1600/v - 1600/(v+400) = 2/3 leads to v^2 + 400v - 960000 = 0. Factoring gives (v+1200)(v-800) = 0, so v = 800 km/h.

AI explanation

Let the usual speed of the plane be v km/h, so the usual time taken is 1600 divided by v hours. To compensate for the 40 minutes lost, which is 2/3 of an hour, the new time becomes 1600 divided by v plus 400 hours, and this time is 2/3 of an hour less than the usual time. Setting up the equation, 1600 divided by v minus 1600 divided by v plus 400 equals 2/3, and solving yields the quadratic equation v squared plus 400v minus 960000 equals 0. Factoring this equation gives v equals 800 or v equals negative 1200, and since speed must be positive, the usual speed is 800 km/h.

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