Question 866231
Each car started at the same time at the beginning of a straight race course.
 When Janis's car crossed the finish line, it was ahead of Jimi's car by 24 inches and was ahead of Dio's car by 32 inches.
 When Jimi's car crossed the finish line it was ahead of Dio's car by 10 inches. How many inches long is the race course? 
:
Let d = distance of the race course in inches
:
The relationship of Jimi's car and Dio's car when Janis crosses the finish line can be expressed:
{{{((d-24))/((d-32))}}}
The relationship of Jimi's and Dio's car when Jimi crossed the finish line can be expressed
{{{d/((d-10))}}}
The two relationships are equal therefore
{{{((d-24))/((d-32))}}} = {{{d/((d-10))}}}
cross multiply
d(d-32) = (d-24)(d-10)
d^2 - 32d = d^2 - 10d - 24d + 240
d^2 - 32d = d^2 - 34d + 240
combine as follows
d^2 - d^2 - 32d + 34d = 240
2d = 240
d = 120 inches is the length of the course
:
:
Did this make sense to you?