Question 490838
in order to qualify for finals in racing event, a race car must achieve an average speed of 250km/hr on a track with a total length of 1600m.
if a particular car covers the first half of the track at an average speed of 230km/hr, what minimum average speed must it have in the second half of the track in order to qualify
:
Let s = min average speed for the 2nd half of the track
Change the distances to .8 km and 1.6 km
Write a time equation, Time = dist/speed
:
{{{.8/230}}} + {{{.8/s}}} = {{{1.6/250}}}
multiply by 57500s (230*250) to clear the denominators, results:
250s(.8) + 57500(.8) = 230s(1.6)
200s + 46000 = 368s
46000 = 368s - 200s
46000 = 168s
s = {{{46000/168}}}
s = 273.8 km/hr to average 250 km.hr
:
:
You can confirm this by finding the actual times
{{{.8/230}}} + {{{.8/273.8}}} = {{{1.6/250}}}