Question

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

Answer 1

Answer:

12.4m

Step-by-step 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:

$4x+\frac{2}{3} x=\frac{14}{3}x$

So now our equation looks like this:

$\frac{14x}{3}=86.8$

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

$\frac{14x}{3}*3=86.8*3\\ 14x=260.4\\\frac{14x}{14}=260.4/14\\ x=18.6$

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

Engine length = 2/3 Carriage length

$E=\frac{2}{3}x\\ E=\frac{2}{3} (18.6)\\E = 12.4m$

Hope this helped!

Answer 2

Length of a carriage = x

Length of four carriages = 86.8 m

Length of each carriage =

$86.8 \div 4 \: m \\ = \: 21.7 \: m$

Length of one carriage = 21.7 m

Length of the engine =

$= \frac{2}{3} x$

$= \frac{2}{3} \times 21.7$

$= 43.4 \: m$

$43.4 \div 3 \: m \\ = 14.4666666667 \: m$

∴ The length of the engine is 14.4666666667 m .