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:
[tex]4x+\frac{2}{3} x=\frac{14}{3}x[/tex]
So now our equation looks like this:
[tex]\frac{14x}{3}=86.8[/tex]
Now all we need to do is multiply both sides by 3 and then divide both sides by 14 to isolate and solve x:
[tex]\frac{14x}{3}*3=86.8*3\\ 14x=260.4\\\frac{14x}{14}=260.4/14\\ x=18.6\\[/tex]
Now that we know the carriage length, we can use it to find the engine length:
Engine length = 2/3 Carriage length
[tex]E=\frac{2}{3}x\\ E=\frac{2}{3} (18.6)\\E = 12.4m[/tex]
Hope this helped!
