Words to algebra II average speed

GRE Quant Problem Solving
1

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Presented solution:
Let the average speed of the train be x. We have

0.8×85.3+0.2×57.3=x

Notice that we need to “weigh” the train speeds - as most of the journey was completed at a certain speed - with a small fraction being completed at a reduced speed (in this case due to “low fuel”).

Solving for x, we x=79.7.

About this question:

Initially, we didn’t specify the “time” bit of the question. However, a Reddit user correctly pointed out that if we were to assume distance instead (as could be reasonably assumed with the original formulation of the question), we can’t quite take the weighted average as we did here. See this thread if you’re curious to know why. Fixing this ambiguity made the question look a bit awkward, but we had to do it.

Question: Does multiplying the individual average speeds by time, as done above, not give you the distance instead? I do not get why this is the right answer.

2

I don’t get what you mean by that.

3

For example, does 85.3*0.8h not give the distance traveled in that time instead?
How do we get average speed when we’ve just multiplied average speed by something else?

4

Yes, that is, in 0.8h time

5

So, should adding both values not give total distance? How does it give the average speed instead?

6

What is the time taken in the first leg? It’s 0.8h, not 0.8. So,

0.8k×85.3+0.2k×57.3

does give you the distance covered by the train. You divide by k to find the average speed.

The equation we gave is

0.8×85.3+0.2×57.3

Notice that we already divided by k.

7

Got it. Thanks.