Here’s a word problem for you:

Our black-widow lashup of Southern Pacific F-3 diesels idles in the afternoon sun at Bena in 1952 at the head of a seventy-car string. We are the fifth (and final) section of train 804 (meaning there are four sections ahead of us, the fourth section 10 minutes down the line). It is now 1:40PM. As head-end engineer, I’ve gone back to meet with my two helper engineers (midtrain and rear) to discuss our next move.

Positionally, we are located as follows:

Kern Jct (Bakersfield) – 10 minutes behind us

Bena (where we are at)

Caliente (15 minutes ahead of us)

Woodford (30 minutes ahead of us)

Mojave (40 minutes ahead of us)

In our hands are copies of the following order:

ENGINE 4255 RUN EXTRA MOJAVE TO KERN JCT

AND MEET FOURTH 804 AT WOODFORD

AND HAS RIGHTS OVER FIFTH 804 MOJAVE TO BENA

AND WAIT AT

MOJAVE UNTIL 1:30PM

WOODFORD UNTIL 1:45AM

CALIENTE UNTIL 2:05AM

So…

What to do? Should we advance against oncoming engine 4255? Is it safe? Will we crash into him?

First plan: ENGINE 4255…HAS RIGHTS OVER FIFTH 804 MOJAVE TO BENA. Seems rather conclusive. 4255 is advancing against us headlong, as he has rights since leaving Mojave at 1:30PM (that WAIT UNTIL bit) to our location at Bena. We can’t move and so we sit. Minutes pass.

Second plan: The crew is sitting around when the mid-train helper engineer (a more daring sort) figures, “Hey, we could have run for Caliente!” “But he has rights over us,” the conductor and I both warble. “He’ll cream us!” “But we know he CAN’T leave Caliente until 2:05am, so he CAN’T run into us!”

The conductor and I look at our orders from that angle and decide, yes, he was right, but not soon enough. It’s now 1:50pm. If we run for Caliente now, we’ll just get there when he’s pulling out – we might smash into him on the edge of town.

“We’ll, we shoulda,” Mid-train grouses.

We sit, destine to remain in Bena for the passing of 4255 at 2:20pm or so, when it hits me.

“Wait a minute – Fourth 804 was ten minutes ahead of us!”

“So?” the conductor says.

“The order states 4255 must meet 804/4 at Woodford. That’s thirty minutes up. Since he was ten minutes head of us when we got here at 1:40, he’ll reach Woodford by Woodford by 2pm, Then it will take 4255 fifteen minutes run to Caliente. That’s… 2:15pm!”

We look at our watches. 1:55pm. We can be in Caliente by 2:10pm

We run for our cabs. A minute later, we are rattling out of Bena and onto the main, pushing the posted limits…