Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is
Explanation:
Let the speed of the slower ship be x km/hr. Distance travelled by it in 2 hours = 2x kms
Speed of faster ship = (x + 6) km/hr. Distance travelled by it in 2 hours = 2(x + 6) kms
⇒ (2x)2 + (2(x + 6))2 = (60)2 ⇒ 4x2 + 4(x2 12x + 36) = 3600 ⇒ 8x2 + 48x + 144 = 3600 ⇒ 8x2 + 48x - 3456 = 0 ⇒ x2 + 6x - 432 = 0 ⇒ (x + 24)(x - 18) = 0 ⇒ x = 18 (-24 is rejected)
∴ Speed of slower person is 18 km/hr
Hence, option (a).
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