Question 44601
THE NUMBERS GIVEN IN THIS PROBLEM ALL LEAD TO FRACTIONS INVOLVING HRS,MTS AND SECS.ARE YOU SURE YOU GOT THE NUMBERS RIGHT?IS DISTANCE BETWEN P AND Q =34 KM OR 35 KM?
Two towns P and Q are 35 km apart. Peter starts cycling from P towards Q at 12 p.m. at 20 km/h until he is 16 km from P, when he changes speed so that he arrives at Q at 2 p.m. John leaves Q at 12:30 p.m. and cycles to P at a constant speed 26 km/h, find
a)the time when Peter and John meet.
b)the distance that they will meet 
PETER TRAVELS STARTING FROM P AT 12=00 PM GOING AT 20 KMPH FOR 16 KM
TIME TAKEN =16/20=0.8 HRS=0.8*60=48 MTS….THAT IS AT 12 =48
BALANCE DISTANCE TO Q =35-16=19 KM.
TIME TAKEN TO REACH =2=00 PM THAT IS 14=00 HRS
TRAVEL TIME  IS 14=00 - 12 =48 =1 HR12 MTS. = 1 +12/60 HRS =6/5 HRS.
PETERS SPEED DURING THIS TRAVEL =19/(6/5)=5*19/6=95/6 KMPH
JOHN LEAVES Q AT 12=30 PM.
TILL 12=48 HE TRAVELS FOR 12=48 -12=00=18 MTS=18/60 HRS =0.3 HRS.
DISTANCE TRAVELLED BY JOHN DURING THIS PERIOD AT 26 KMPH=26*0.3=7.8 KM
HENCE DISTANCE OF SEPERATION BETWEEN PETER AND JOHN AT 12 = 48 IS (35-16)-7.8=11.2 KM
THEIR RELATIVE SPEED WHILE TRAVELLING IN OPPOSITE DIRECTIONS =95/6 +26=(95+156)/6=251/6 KMPH
TIME TAKEN TO MEET =11.2/(251/6)=67.2/251 HRS = 16.06 MTS
HENCE PETER AND JOHN MEET AT 12=48 + 16.06 MTS..THAT IS AT 13 HRS.04 MTS.36 SEC
THE DISTANCE AT WHICH THEY MEET =16.06*95/6=4.24 KM THAT IS AT 16+4.24=18.24 KM FROM P.