In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?
Answer: A
Let X be the length of the course
according to the question,
A beats B by 15 metres and C by 29 metres
Applying this,
If A runs X metres, B runs (X-15) and C runs ( X-29) metres.
B and C together run, B runs X metres and C runs (X-15)
=> If B runs 1 metre, C runs X-15/X
=> B runs X-15 m, C runs (X-15/x) * (X-15)
APPLYING THIS,
X-29 = (X-15)(X-15) / X
Solving,
X⊃2; -29X= X⊃2; – 30 X + 225
X = 225
Thus, length of the course is 225 metres.