<PRE><B>Question 1201640</B>
A cyclist decides to ride from bugibba to mellieha ,a distance of six kilometres .The average speed is x kilometres per hour .On his return journey from mellieha to bugibba  he rides 12 kilometres per hour faster and completes the journey 15 minutes more quickly .Form and  solve an equation in X(Ans =12km/hr)



bugibba to mellieha ,a distance of 6 km
speed x km/h

time = 6/x km/h

from mellieha to bugibba distANCE = 6KM
 he rides 12 kilometres per hour faster = (x+12)
Time return = 6/(x+12)

Time onwards - time return = 0.25

{{{( 6/x) - 6/(x+12)= 0.25}}}

{{{( 6(x+12)-6x)/x(x+12) = 0.25}}}   

{{{(6x + 72 -6x)/x(x+12) = 0.25}}}

{{{72/(x(x+12)) =0.25}}}    (0.25=1/4)

72 =  (1/4) *x(x+12)

4*72 = x^2 +12x

288 = x^2+12x

x^2+12x-288 =0

x^2+24x-12x-288 =0


x(x+24)-28(x+24) =0

(x+24)(x-12) =0

x = -24 or 12 speed cannot be negative
 
x=12 km/h



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