The answer is simple. One towrope must go over the top of the other boat and its towrope. But which one? Also, isn’t it going to get a bit tedious doing this 100 times? In any case, there is a huge amount of work involved. Let’s work it out:-

- If boats travel at the same speed in both directions, then when a towrope has to go over another boat and tow rope, It travels half the length of that towrope and boat, while the other boat travels under its tow rope for half the distance too. How much is half the distance? (Answer)
- If each boat passes its tow rope over half of the boats coming the other way, what is the total distance it travels with its tow rope going over something else? (Answer)

There’s another problem with 200 boats travelling the canal. At the moment, there are 12 swing bridges between Liverpool and Wigan, but in those days, there were many, many more. To simplify our arithmetic, let’s imagine there are 10. Now consider our 200 boats, each opening and closing each swing bridge.

- How many swing bridge operations (open = 1, close = 1) is that? (Answer) It’s a HUGE amount of work! And what about all the road traffic that is disrupted?

Surely we can cut down on all this work. Let’s imagine the boatmen decide to work together in groups of 10, and we call the 10 boats working together a “convoy”. Let’s see what we can do.

The fist thing is, the horse of the second boat walks alongside the stern of the first boat, and the horse of the third boat walks alongside the stern of the second boat, and so on. Now the person leading the horse is able to chat with the person steering the boat in front.

When the convoy gets to a closed swing bridge, the whole convoy closes up and pulls into the bank on the towpath side. They wait for a convoy coming the other way, then open the bridge to let them through. A coal boat is about 25m long, so 10 boats parked bow to stern is 250m. The crews of the parked boats can lift the tow rope over the open stern of their own boats, so that the moving boats don’t need to slow down.

Once the moving convoy is through, the stopped convoy can go through, and close the bridge behind it.

Let’s work out what we gain by this convoy system:

- First off, we’ve got a more sociable, less monotonous working day.
- Secondly, because 20 boats go through a bridge each time it’s opened, each bridge is only opened 10 times a day. How many bridge operations is that? (Answer) How many less than 4,000 is that? (Answer)
- Each convoy stops at half of the swing bridge, and passes its tow ropes over a convoy at the other half. What is the total distance a boat travels with its tow rope going over something else? (Answer)

By travelling in convoy like this, the number of times bridges must be opened and closed is reduced by 9/10 (90%) and the distance travelled with the towrope over another boat, towrope, boat or horse is reduced by more than 2/3.

We don’t know that the boatmen of old worked like this, but it makes sense to do so because it saves a lot of work, and if we can work it out, so could they.

Convoys

It is about 34 miles (55 Km) from Wigan Pier to Stanley Locks in Liverpool. If there are 201 boats travelling the length of this canal at any time, what is the average distance between them? (Answer)

Until the middle of the 19th century, all canal boats were towed by horses. The towing rope was approximately 25m long, and a coal boat is 25m long. Try to imagine this scene. There are 100 boat travelling North and one hundred boats travelling South, all of them being towed by horses. The horses are all on the same towpath. How do they get past each other without tangling the towropes?