Najip, Kumar and Gurmit started jogging at the same time from the same starting-point round a circular track. Najip and Kumar jogged in a clockwise direction and Gurmit jogged in an anti-clockwise direction. Gurmit took 5 minutes to complete each round. Gurmit met Najip after every 3 minutes. Gurmit met Kumar after every 2 minutes. The jogging speed of each person remained the same throughout.
(a) What was the ratio of Gurmit's speed to Najip's speed to Kumar's speed?
(b) When Gurmit and Najip met again at the starting-point after 15 minutes, Kumar had already jogged 3.6 km. What is the circumference of the circular track?
G [ ][ ][ ][ ][ ] 5 min, 1 round
3 min Constant Time
G [ ][ ][ ] SG : SN = DG : DN
[ ][ ] N = 3 : 2
= 6 : 4
2 min Constant Time
G [ ][ ] SG : SK = DG : DK
[ ][ ][ ] K = 2 : 3
= 6 : 9
SG : SN : SK = DG : DN : DK Constant Time
= 6 : 4 : 9
a) The ratio of Gurmit's speed to Najip's speed to Kumar's speed was 6 : 4: 9.
DG : DN : DK = 6 : 4: 9
= 3 : 2 : 4.5
When Gurmit and Najip met again at the starting-point, Gurmit would have run 3 rounds while Najip 2 rounds and Kumar 4.5 rounds.
4.5 rounds --> 3.6 km
1 round --> 1/4.5 x 3.6 = 0.8 km
b) The circumference of the circular track was 0.8 km.