=10m/s Let the time taken by A to finish the race be t seconds and the speed of A be vA m/s. Distance covered by A in t seconds =1000m=vA×t Distance covered by B in t seconds =900m=vB×t ∴
VA
VB
=
1000
900
⇒VA=
1000
900
×10=
100
9
m/s Time taken by A to finish the race in the 2nd case =
100
100
9
=90 seconds Time taken by B to finish the race in the 2nd case
=
450
10
+
550
5
=45+110=155 seconds
Therefore, time by which A beat B =155−90=65 seconds