Question
Two classmates R and S stand at points U and V
respectively. R starts toward V from U at a speed of (x – 5) km/h. After 3 hours, S starts toward U from V at a speed of (x + 5) km/h. They meet exactly at the midpoint of UV. If UV = 360 km, find the time taken by R to go from U to V.Solution
ATQ, Distance covered by R in 3 hours = (x – 5) × 3 = 3(x – 5) km Remaining distance between them = 360 – 3(x – 5) = 360 – 3x + 15 = (375 – 3x) km Time of meet after S starts = (375 – 3x)/(2x) hours According to question, [(375 – 3x)/(2x)] × (x + 5) = 360/2 (375x + 1875 – 3x² – 15x) = 360x ⇒ –3x² + 1875 = 0 3x² = 1875 x² = 625 x = 25 Speed of R = 25 – 5 = 20 km/h Therefore, required time = 360/20 = 18 hours
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