Question
Two trucks start from depots C and D facing each other.
Driver 1 (from C) moves toward D at (x – 7) km/h. After 3 hours, Driver 2 (from D) heads toward C at (x + 7) km/h. They meet right at the midpoint of CD. If CD = 504 km, find Driver 1’s total travel time from C to D.Solution
ATQ, Distance covered by Driver 1 in 3 hours = 3(x – 7) km Remaining distance = 504 – 3(x – 7) = 504 – 3x + 21 = (525 – 3x) km Time of meet after Driver 2 starts = (525 – 3x)/(2x) hours According to question, [(525 – 3x)/(2x)] × (x + 7) = 504/2 (525x + 3675 – 3x² – 21x) = 504x ⇒ –3x² + 3675 = 0 x² = 1225 x = 35 Speed of Driver 1 = 35 – 7 = 28 km/h Therefore, required time = 504/28 = 18 hours
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