After Sam and Pat bike in opposite directions for 212 hours

After Sam and Pat bike in opposite directions for 2&1/2 hours, they are 80km apart. If Pat\'s rate is 2 km/h more than Sam\'s rate, find how far each travels.

Solution

RELATIVE SPEED WHILE GOING IN OPPOSITE DIRECTIONS =SUM OF SPEEDS=
LET SAMS SPEED = S KMPH....PAT\'S SPEED IS S+2 KMPH
REL.SPEED =S+S+2=2S+2=2(S+1)
DISTANCE OF SEPERATION =80 KM
TIME =2.5 HRS
SO 2.5=80/{2(S+1)}=40/(S+1)
S+1=40/2.5=16
S=16-1=15 KMPH....IN 2.5 HRS SAM GOES =15*2.5=37.5 KM
P=S+2=17 KMPH.....IN 2.5 HRS PAT GOES =17*2.5=42.5 KM