Question

two cyclists, Elisa May and dhey-dhey , start at the same time from opposite ends of a course that is 45 miles long. Elisa nay is riding at 14mph and dhey-dhey at 16mph. How long after they begin to meet?

Answer 1

The distance that Elisa May travels is given by the formula:\[x_1=14 t\] and dhey-dhey's distance:\[x_2=16 t\]When the two cyclicts meet, Elisa May has travelled x miles and dhey-dhey's travelled (45-x) miles.
That gives us two equations:\[x=14t\]\[45-x=16t\]Let's solve the system, now
\[x=14t\]\[45-14t=16t\]
\[x=14t\]\[30t=45\]
\[x=14t\]\[t=\frac{45}{30}\]
\[x=14\times \frac{45}{30}\]\[t=\frac{45}{30}\]
\[x=21\]\[t=\frac{45}{30}\]So the two cyclist meet after Elisa May has travelled 21miles.