QQuestion
Speed of A is 1 m/sec more than that of B. A reaches 2 seconds earlier than B in 180m sprint competition. Find the speed of B in m/sec.
✓Answer
Let speed of B = x m/s. Then speed of A = (x + 1) m/s.
Formula: Time = \frac{\text{distance}}{\text{speed}}
Time of B = \frac{180}{\text{x}},
Time of A = \frac{180}{\text{x + 1}}.
Given time difference 2 s:
\frac{180}{\text{x}} − \frac{180}{\text{x + 1}} = 2.
180 × (\frac{1}{\text{x}} − \frac{1}{\text{x+1}}) = 2
⇒ 180 × \frac{\text{x+1 − x}}{\text{x(x+1)}} = 2
⇒ \frac{180}{\text{x(x+1)}} = 2
⇒ x(x+1) = 180/2 = 90.
Hence x² + x − 90 = 0.
⇒ x² + (10 – 9)x − 90 = 0
⇒ x² + 10x – 9x − 90 = 0
⇒ (x + 10)(x – 9) = 0
x = 9 or x = -10 (reject)
Therefore speed of B = 9 m/s.
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