Bunuel wrote:

A train left a station P at 6 am and reached another station Q at 11 am. Another train left station Q at 7 am and reached P at 10 am. At what time did the two trains pass one another?

(A) 7:50 am

(B) 8:13 am

(C) 8:30 am

(D) 8:42 am

(E) 9:03 am

Assign a distance. Then use the "gap" and relative speed approach

Distance?Call the trains B and C.

They travel the same distance.

B takes 5 hours (from 6 to 11 a.m.)

C takes 3 hours (from 7 to 10 a.m.)

Let distance between P and Q = 15 miles (LCM of 5 and 3)

Use each train's time to find rates.

(1) Each train's rate?

\(r*t=D\)

B, rate: \((r*5hrs)=15mi\)

B, rate: \(r=\frac{15mi}{5hrs}=3\) mph

C, rate: \((r*3hrs)=15mi\)

C, rate: \(r=\frac{15mi}{3hrs}=5\) mph

(2) Distance "gap" between B and C?

B is at station P

C is at station Q

Initial distance = 15 miles

But B travels alone for 1 hour

-- B covers \((3mph*1hr)=3\) miles

-- B shortens the distance between them from 15 to 12 miles

That 12 miles is a "gap." When B and C at relative speed cover the distance, they close that gap and pass one another.

(3) Relative rate/speed?

Opposite directions (towards or away): ADD rates

Relative rate/speed: \((3+5)=8\) mph

(2) Time required for them to pass? \(R*T=D\), so

\(T=\frac{D}{R}\)

\(T=\frac{12mi}{8mph}=\frac{3}{2}=1.5\) hours

(4) Clock time at which they pass one another?

Calculate clock time from the start time of the

second train (then

both trains are moving)

Train C left at 7:00 a.m.

1.5 hours later is 8:30 a.m.

Answer C