Multiple choice

A train is travelling at a constant speed and covers 715 km. But to reach the next station (which is at the same distance as the first station) 2 hours earlier, it increases its speed by 10 km/hr. Which of the following represents the original speed of the train?

  1. 50 km/hr

  2. 55 km/hr

  3. 60 km/hr

  4. 66 km/hr

  5. 70 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed be v. Time taken = 715/v. New time = 715/(v+10). Given 715/v - 715/(v+10) = 2. Solving 7150 = 2v(v+10) leads to v^2 + 10v - 3575 = 0. Using the quadratic formula, v = (-10 + sqrt(100 + 14300)) / 2 = (-10 + 120) / 2 = 55 km/hr.

AI explanation

Let the original speed be v kmph; the distance of 715 km gives the initial time as 715 divided by v. The new time is 715 divided by (v plus 10). The difference in time is 2 hours, so (715 divided by v) minus (715 divided by (v plus 10)) equals 2. Solving 715 times (v plus 10) minus 715v equals 2v times (v plus 10) results in v squared plus 10v minus 3575 equals 0, which factors to (v plus 65)(v minus 55) equals 0. This gives the valid result of 55 km/hr.

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