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.

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:

So now our equation looks like this:

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

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

Engine length = 2/3 Carriage length

Hope this helped!

Length of a carriage = x

Length of four carriages = 86.8 m

Length of each carriage =

Length of one carriage = 21.7 m

Length of the engine =

∴ The length of the engine is 14.4666666667 m .

6: 07 is your answer

step-by-step explanation:

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)