A cyclist moves non-stop from a to b, a distance of 14km, at a certain average speed. if his average speed reduces by 1km/h, then he takes 20min more to cover the same distance. the original average speed of the cyclist is
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let original speed be x km per hr
frm A to B distance is 14km
time taken to travel frm a to b = dis/speed = 14/ x hr
if the speed reduces to 1 km per hr then the new speed = x - 1km per hr
14 / x-1 =14/x + 1/3
14/x-1 - 14 /x = 1/3
14 [ (1/x-1) - ( 1/x )] = 1/ 3
14 [x-(x-1) / x(x-1) ] = 1/3
14 / x(x-1) = 1/3
x(x-1 ) = 42
x^2 - x - 42 = 0
x^2 - ( 7 - 6 )x - 42 = 0
x^2 - 7x + 6x - 42 = 0
x(x-7) + 6 ( x-7) =0
( x-7 ) ( x+ 6) =0
so either x=7 or x= -6
since the speed can not be negative so the original speed of the cyclist is
7 km/hr
frm A to B distance is 14km
time taken to travel frm a to b = dis/speed = 14/ x hr
if the speed reduces to 1 km per hr then the new speed = x - 1km per hr
14 / x-1 =14/x + 1/3
14/x-1 - 14 /x = 1/3
14 [ (1/x-1) - ( 1/x )] = 1/ 3
14 [x-(x-1) / x(x-1) ] = 1/3
14 / x(x-1) = 1/3
x(x-1 ) = 42
x^2 - x - 42 = 0
x^2 - ( 7 - 6 )x - 42 = 0
x^2 - 7x + 6x - 42 = 0
x(x-7) + 6 ( x-7) =0
( x-7 ) ( x+ 6) =0
so either x=7 or x= -6
since the speed can not be negative so the original speed of the cyclist is
7 km/hr
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