Question

An engine pulls four identical carriages. The engine is the length of 2/3

a carriage and the total length of the train is 86.8 m. Find the length
of the engine.​

Answer 1

Length of a carriage = x

Length of four carriages = 86.8 m

Length of each carriage =

`86.8 / 4 \: m \\ = \: 21.7 \: m`

Length of one carriage = 21.7 m

Length of the engine =

`= (2)/(3) x`

`= (2)/(3) * 21.7`

`= 43.4 \: m`

`43.4 / 3 \: m \\ = 14.4666666667 \: m`

∴ The length of the engine is 14.4666666667 m .

Answer 2

12.4m

Explanation:

In order to solve this equation, we can use the length of a carriage as our unknown value (using the engine is a bit more difficult). The questions says that the whole train: 4 carriages and an engine = 86.8m

If we represent carriage length as 'x', we can write the following equation:

4x (length of 4 carriages) + (2/3)x (length of engine as it is 2/3 of a carriage) = 86.8m

4x+(2/3)x = 86.8

From here we can combine into one fraction:

`4x+(2)/(3) x=(14)/(3)x`

So now our equation looks like this:

`(14x)/(3)=86.8`

Now all we need to do is multiply both sides by 3 and then divide both sides by 14 to isolate and solve x:

`(14x)/(3)*3=86.8*3\\ 14x=260.4\\(14x)/(14)=260.4/14\\ x=18.6\\`

Now that we know the carriage length, we can use it to find the engine length:

Engine length = 2/3 Carriage length

`E=(2)/(3)x\\ E=(2)/(3) (18.6)\\E = 12.4m`

Hope this helped!