8. A man walks for x hours at a speed of (x+1) km/h and cycles for (x - 1) hours at a speed of (2x + 5) km/h. If the total distance travelled is 90 km, find x.
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We know that, Distance = Speed x Time
∴ 90= x(x + 1) + (x-1)(2x+5)
⇒ 90= x² + x + 2x² + 5x - 2x - 5
⇒ 90 + 5= 3x² + 4x
⇒ 3x² +4x - 95 = 0
⇒ 3x² +19x - 15x - 95 = 0
⇒ x(3x + 19) - 5(3x + 19) = 0
⇒ (3x + 19) (x - 5) = 0
⇒ 3x + 19 = 0, x - 5 = 0
⇒ x = -19/3, x = 5
Rejecting x = -19/3; x = 5
∴ 90= x(x + 1) + (x-1)(2x+5)
⇒ 90= x² + x + 2x² + 5x - 2x - 5
⇒ 90 + 5= 3x² + 4x
⇒ 3x² +4x - 95 = 0
⇒ 3x² +19x - 15x - 95 = 0
⇒ x(3x + 19) - 5(3x + 19) = 0
⇒ (3x + 19) (x - 5) = 0
⇒ 3x + 19 = 0, x - 5 = 0
⇒ x = -19/3, x = 5
Rejecting x = -19/3; x = 5
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