First condition,        "If both start at 10 am they will meet at 3 pm." means that

5x + 5y = 960  kilometers   (1)   (they cover the distance in 5 hours, from 10 am to 3 pm)



The second condition    "If Murray starts at 6 am and Mary starts at 10 am they will meet at noon."  means

6x + 2y = 960               (2)   (Murray is on the way during 6 hours, while Mary is on the way only 2 hour before they meet each other)



So, you have this system of 2 equations in 2 unknown

5x + 5y = 960,   
6x + 2y = 960,

which you can easily solve by any method.

5x + 5y = 960____5(x + y) = 5(192)______x + y = 192 ------- eq (i)

2x + 6y = 960____2(x + 3y) = 2(480)_____x + 3y = 480 ------ eq (ii)

2y = 288 ------- Subtracting eq (i) from eq (ii)



You should also get:  

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