SOLUTION: Please help me solve this question. John leaves his house at 7:00 am. His sister, Mary leaves the house at 8:30 am and tries to catch up with John. She is walking 2 km/h faster th

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Question 1184521: Please help me solve this question.
John leaves his house at 7:00 am. His sister, Mary leaves the house at 8:30 am and tries to catch up with John. She is walking 2 km/h faster than him on the same route in the same direction. If they both kept in the same route, Mary could reach John 3 hours after she left. Find John and Mary’s speed.
Found 2 solutions by Edwin McCravy, mccravyedwin:
Answer by Edwin McCravy(20054) About Me  (Show Source):
Answer by mccravyedwin(406) About Me  (Show Source):
You can put this solution on YOUR website!

John's rate = r
Mary's rate = r+2
Mary's time till they meet = 3  
John's time till they meet = 4.5 (7:00 am to 8:30 is an hour and a half,
                                  and 3+1.5 = 4.5

       rate  x  time  =  distance
-------------------------------------
John     r      4.5    =   4.5r
Mary    r+2      3   =    3(r+2)      

The distances are equal, so

4.5r = 3(r+2)

Multiply both sides by 10 to clear the decimal

45r = 30(r+2)

Divide both sides by 15

3r = 2(r+2)
3r = 2r+4
 r = 4 km/h = John's rate.

Mary's rate = 2 km/h + 2 km/h = 4 km/h

Edwin