8. Brian and Luke race over 50 metres. Brian runs so that it takes him a seconds to run
1 metre. Luke runs so that it takes him b seconds to run 1 metre. Luke wins the race by
1 second. The next day, they race again over 50 metres (and again at the same speeds)
but Luke gives Brian a 3-metre start so that Brian only runs 47 metres. Luke wins this
race by 0.1seconds. Find
(i) the values of a and b
(ii) Luke's speed.
