Multiple choice

The speeds of two buses, Bus P and Bus Q, are p km/h and q km/h, respectively, where p > q. The speeds p and q are the roots of the equation x2 - 144x + 5,120 = 0. Let TP and TQ be the usual times taken by Bus P and Bus Q, respectively, to cover a certain distance D km. If their speeds are interchanged for the same distance D, Bus P takes (TP + 3) hours and Bus Q takes (TQ - 3) hours. Find TP + TQ.

  1. 24 hours

  2. 25 hours

  3. 26 hours

  4. 27 hours

  5. 28 hours
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D Correct answer
Explanation

Roots p, q of x^2 - 144x + 5120 = 0. p+q = 144, pq = 5120. Solving gives 80 and 64. D/q - D/p = 3 and D/p - D/q = -3. Using D/64 - D/80 = 3 => (5D-4D)/320 = 3 => D = 960. T_P = 960/80 = 12, T_Q = 960/64 = 15. T_P + T_Q = 12 + 15 = 27.

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