Question 869965
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

{{{((3/x) +(1/12)) - (3/(x+(1/2)))= (1/6)}}}

{((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)

{{{72x+36+2x^2+x-72x=4x^2+2x}}}

Simplify

2x^2+x-36=0

{{{2x^2+9x-8x-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