Question
A motorcyclist travels the first
half of his trip at a speed of 4x km/h and the second half at a speed of 4x – 10 km/h. If his average speed for the full journey is 44 km/h, find the value of x. [x > 5]Solution
According to the question, (2 × 4x × (4x – 10)) / (4x + 4x – 10) = 44 ⇒ x(4x – 10) / (8x – 10) = 22 ⇒ 22(8x – 10) = x(4x – 10) ⇒ 176x – 220 = 4x² – 10x ⇒ 4x² – 186x + 220 = 0 ⇒ 2x(2x – 93) – 10(2x – 11) = 0 ⇒ (2x – 10)(2x – 11) = 0 ⇒ x = 11 or x = 5 ∴ x = 11
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