Speed P6

Alfred and Peter jogged to and fro repeatedly along a straight path in a park between two points A and B. Alfred jogged at a uniform speed of 40m/min and Peter at 60m/min. They started jogging from the opposite directions at the same time as shown below.
Alfred----->                                                    <-------Peter
    A--------------------------X-----------------Y----------------B

Distance between X and Y: 200m

They first met one another at point X. The second time they met was at point Y.

a) Find the distance between A and B.
b) If they started jogging at 0715, when did they meet again for the third time?


A1    [ ][ ][ ][ ] X
P1                   [ ][ ][ ][ ][ ][ ]

DA : DP = 4 : 6                      Constant Time
              = 2 : 3

A2                   [                    ]
                                   [   a    ]
      [     10 u - a          ] Y
P2  [               ]

6 u + a : 4 u + (10 u - a) = 2 : 3      Constant Time
3 x (6 u + a) = 2 x (14 u - a)
3 a + 2 a = 28 u - 18 u
5 a = 10 u
a = 2 u

4 u --> 200 m
10 u --> 10/4 x 200 = 500 m

a) The distance between A and B was 500 m.

500 x 5 = 2500 m        Total distance travelled to meet the third time
40 + 60 = 100 m/min   Combined speed

2500 ÷ 100 = 25 min

        25 min
   |--------------|
0715           0740

b) They met again for the third time at 0740.