Multiple choice

A train leaves the station $1$ hour before the scheduled time. The driver decreases its speed by $50$ km/hr. At the next station $300$ km away the train reached on time. Find the original speed of the train.

  1. $100$ km/hr
  2. $150$ km/hr
  3. $125$ km/hr
  4. $200$ km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed be v. Time taken at original speed is 300/v. Time taken at reduced speed (v-50) is 300/(v-50). The difference is 1 hour: 300/(v-50) - 300/v = 1. Solving v^2 - 50v - 15000 = 0 gives (v-150)(v+100)=0, so v=150.

AI explanation

Let the original speed of the train be x km/hr, so the original time for 300 km is 300/x hours. Since the train leaves an hour early and travels at (x - 50) km/hr, the new time is 300/(x - 50) hours. Because the train reaches on time, the one-hour start compensates for the slower speed, giving the equation 300/x + 1 = 300/(x - 50). Solving this yields x = 150.

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