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A driver went $200$ km. For the first $100$ km of the trip, the driver traveled at a speed of $40$ km/h. For the second half of the trip, the driver traveled at a speed of $60$ km/h. What was the driver’s average speed for the entire trip?

I used the average speed formula which is $\text{speed}_\text{average} = \dfrac{\text{total distance}}{\text{total time}}$

& got $\dfrac{200}{\dfrac{100}{40}+\dfrac{100}{60}}$

which resulted into an average speed of $48$ km/h.

My problem is the way I solved the problem, our topic is rational equations & I don't know how to make it like that with a variable. Does anyone have a clue on how to make a rational equation out of this?

X X
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    The speed formula looks very much like a rational equation. Not sure what else you are looking for. – dxiv May 27 '21 at 06:37
  • If you really want to make it "prettier", you can write $$ \frac{200}{\frac{100}{40} + \frac{100}{60}} = \frac{200}{\frac{300}{120} + \frac{200}{120}} = \frac{200}{\left(\frac{5 00}{120} \right)} = \ldots $$ – Matti P. May 27 '21 at 07:43
  • is there a way to have a representation for it so that the rational equation has a variable? – X X May 28 '21 at 09:59

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