At 5pm, Jill leaves New York City and travels toward Boston at an aver

At 5pm, Jill leaves New York City and travels toward Boston at an average rate of 56 miles per hour. At 6pm, Billy leaves Boston and travels toward New York, on the same road as Jill, at an average rate of 50 miles per hour. If the distance between New York City and Boston is 215 miles, at what time do Billy and Jill pass each other?

A. 7:20 pm
B. 7:22 pm
C. 7:25 pm
D. 7:30 pm
E. 8:30 pm

fast approach

1h from 05 to 06 then 1 train travelling at v1+v2 on the remaining distance

\(1+\frac{215-56}{50+56}=1+1.5=2.5h \to 1+1.5=07:30\) more analitical approach

1h at 56 mph -> 56

NY--------1h----------s1-------------t-----------s2-------------B

215-56=159 miles left

s2=159-s1

equate for t

\(\frac{s1}{v1}=\frac{s2}{v2}\)

\(\frac{s1}{v1}=\frac{159-s1}{v2}\)

\(s1*v2=159*v1-s1*v1\)

\(\frac{s1*(v2+v1)}{v1}=159\)

let \(\frac{s1}{v1}=t\)

\(t=\frac{159}{v1+v2}\)

\(t=\frac{159}{106}=1.5h\)

they will meet at \(1+1.5=2.5h \to 07:30\)

edit: updated graphics