SOLUTION: John and Peter leave the cottage by two separate roads, each 3km in length, to go to town. Peter walks 0.5 km/h faster than john. Along the road John meets a friend and stop to tal

Question 869965: John and Peter leave the cottage by two separate roads, each 3km in length, to go to town. Peter walks 0.5 km/h faster than john. Along the road John meets a friend and stop to talk for 5 min, so peter has to wait in town 10 for John to arrive, How fast do John and Peter walk? Show your work. How long does it take John and Peter to travel the Distance? Show your work.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
John and Peter leave the cottage by two separate roads,
d=3 km to go to town.
John speed =x km/h
Peter speed = (x+1/2) km/h
Time taken by john is walking time + 5 minutes = 5/60=> = 1/12 hours
Peter has to wait in town 10 minutes = 10/60 = 1/6 hours
Time taken by John to reach town
t1= d/r =(3/x)+(1/12)
time taken by Peter = 3/(x+(1/2))
Time taken by John - time taken by Peter = 10 minutes = 1/6 hours

{((36+x)/12x)-(6/(2x+1))= (1/6)}}}
LCM of denominator = 12x(2x+1)
Multiply equation by 12x(2x+1)
(36+x)(2x+1) -72x=2x(2x+1)

Simplify
2x^2+x-36=0

x(2x+9)-4(2x+9)=0
(2x+9)(x-4)=0
2x=-9
x=-9/2
x= -4.5 km/h
Ignore
x=4

John speed = 4 km/h
Peter speed =4.5 km/h

Time John = 3/4 +1/12 =10/12=>5/6 hour
Time Peter = 3/(9/2)=> 2/3 hours
Check
5/6 -2/3
=1/6 = 10 minutes

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