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Seeta and geeta cycled towards each other, one from point A and the other from point B, respectively. seeta left a 6 hours later than geeta left point b, and it turned out on their meeting that seeta had travelled 12km less than geeta. after their meeting, they kept cycling with same speed, and seeta arrived at b 8 hours later and geeta arrived at a 9 hours later. find speed of the faster cyclist.
1)4km/hr 2)6km/hr 3)9km/hr 4)12 km/hr
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Answers
Seeta and geeta cycled towards each other, one from point A and the other from point B, respectively. seeta left a 6 hours later than geeta left point b, and it turned out on their meeting that seeta had travelled 12km less than geeta. after their meeting, they kept cycling with same speed, and seeta arrived at b 8 hours later and geeta arrived at a 9 hours later.
Given,
Let v1 represent the velocity of Seeta
Let v2 represent the velocity of Geeta
From given, we have,
t × v1 = 9 × v2 ...........(1)
8 × v1 = (t + 6) × v2 ............(2)
dividing equation (2) by (1), we get,
8 × v1 / t × v1 = (t + 6) × v2 / 9 × v2
8 / t = (t + 6) / 9
t (t + 6) = 8 × 9
t² + 6t = 72
t² + 6t - 72 = 0
solving the above quadratic equation, we get,
t = 6
Substituting the value of "t" in equation (1), we get,
t × v1 = 9 × v2
6 × v1 = 9 × v2
2 × v1 = 3 × v2 ............(3)
Since, Seeta had travelled 12 km less than Geeta
6 × v1 = 12 × v2 - 12
v1 = 2 × v2 - 2
2 × v1 = 4 × v2 - 4 ..............(4)
equating the equations (3) and (4), we get,
3 × v2 = 4 × v2 - 4
∴ v2 = 4 km/hr
v1 = 2 × v2 - 2
⇒ v1 = 2 × 4 - 2 = 6
∴ v1 = 6 km/hr
The speed of the fastest cyclist is 6 km/hr
Therefore, option 2) is correct.