Multiple choice

Rachel can cover a distance of 56 km at some constant speed in a certain time. If she increases her speed by 1 km/hr, she will be able to cover the same distance in an hour less. What would be the time taken by her to cover a distance of 104 km at the increased speed?

  1. 13 hours

  2. 14 hours

  3. 15 hours

  4. 16 hours

  5. 17 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speed be v. 56/v - 56/(v+1) = 1. Solving v^2 + v - 56 = 0 gives v=7. Increased speed = 8 km/hr. Time for 104 km = 104/8 = 13 hours.

AI explanation

Let her original speed be v km/hr and her original time be t hours, so 56 = v*t. With the increased speed, the equation is 56 = (v + 1)(t - 1). Expanding the second equation gives 56 = vt - v + t - 1, and substituting vt = 56 yields 0 = -v + t - 1, or v = t - 1. Substituting this into the first equation gives 56 = (t - 1)*t, so t = 8 hours and the increased speed is 8 km/hr. The time taken to cover 104 km at this increased speed is 104 / 8, which equals 13 hours.

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