Rates

[JbhB682]

Hello

In the Work = rate* time or Distance = rate* time chart

I have always seen Rates in the form of units/time

Example

- 5 litres/ hour
- 2 kms / minutes
- 10 units / second

Just wondering in that case.. What is the concept of time / unit ?

Is that just 1/R or T/W in the w.r.t chart ?

Per below, S2 is talking about minute / km which threw me off as I have only seen units for Rates as km / minute s


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Source- GMAT prep

Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1 mile = 1.6 kilometers, rounded to the nearest tenth.)

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour.

(2) On average, it took Pei more than 9 minutes per kilometer to walk this distance

[Sage Pearce-Higgins]

There are a couple of possibilities here: you could convert the "time per distance" unit into a "distance per time" unit by taking the reciprocal. I.e. 9 minutes per kilometer is equal to 1/9 kilometers per minute.

Alternatively, you could make a different table: in this case the formula would be rate x distance = time. Now, before you potentially get mixed up by trying to memorize a new strategy, I strongly encourage you to understand where rate formulas come from. Essentially a rate is "something per something", it could be miles per hour, or donuts per day, or neutrons per millisecond. As you observed, the time is often second, but it doesn't have to be: think of seconds per lap, or minutes per mile, or even something without time, such as coffees per worker. In all these cases, the way of calculating the rate is to interpret "per" as division. The formula for miles per hour is 'number of miles / number of hours'; the formula for seconds per lap is 'seconds / laps'; the formula for coffees per worker is 'number of coffees / number of workers'. In fact, if you understand this, then there isn't really a 'formula' at all, so much as simply an understanding of what the rate is expressing.

You can see that my preferred approach to rates is through understanding; I'm quite skeptical of the RTW table as it's easy to misapply. Additionally, I encourage you to draw a connection between rates and another mathematical concept with a similar name...ratios. Looking at statement (1) below, if Pei covers less than 6.4 km in one hour, then he'll cover ??? in 2 hours.

Please post again if you have any follow up questions.

[Mahboubian]

When converting units like "time per distance" into "distance per time," you're dealing with reciprocal relationships. A good way to visualize this is to think about the example you mentioned: if it takes 9 minutes to cover one kilometer, then in one minute, you would cover 1/9 of a kilometer. This approach helps in understanding how fast something happens relative to a unit of measurement.

[Whit Garner]

Nice suggestion Mahboubian!

I find that it can also help to consider the units in rate problems as a fraction. So 9 minutes every 1 kilometer is the same as the ratio: 9 min / 1 km. That way you can simply view the reciprocal if you wanted your units in km / min: 1 km / 9 min or as you said, 1/9 km/min.


Whit