On Monday, it took Helen 3 hours to do a page of science
homework exercises. The next day she did the same number
of exercises in 2 hours. If her average rate on Monday was p
exercises per hour, what was her average rate the next day, in
terms of p?
I know that the answer is 3/2 p exercises per hour, but I don't completely understand how that is.
The part that is confusing me is the wording of the question when it says "average rate" and "terms of p". I'm thinking "terms of p" is equivalent to saying units per measure ie. feet squared, etc.
Can someone please thoroughly explain the though process behind achieving the answer?
total = p * 3
total = q * 2
where q is new improved rate
so
q * 2 = 3 * p
q = (3/2) p = 1.5 p
" ....The next day she did the same number of exercises ...... "
This clues me in to set a total number of exercises, which I call "total" that is the same both days.
if she does 3 execises per hour I call that rate p per hour
then p exercises/hour * 3 hours = total exercises done
then the next day she works at another rate, q exercises per hour
and we are told that she gets the total done in 2 hours
so
q exercises/hour * 2 hours = that same total
Also what kind of problem is this? a rate of change?
What word told you to multiply 3 and pe and q and 2 instead of divide? and then why did you set them equal to each other?
Sure, let me break it down for you and hopefully add a bit of humor along the way!
Firstly, when they talk about Helen's average rate on Monday being "p exercises per hour," they are referring to how many exercises Helen did in one hour. So, if her average rate is p exercises per hour and it took her 3 hours to do a page of science homework exercises, we can say that she did 3p exercises in total on Monday.
Now, let's move on to the next day. They tell us that Helen did the same number of exercises in 2 hours. This means she did 3p exercises in 2 hours, or 3p/2 exercises per hour. So, her average rate on the next day is indeed 3/2 p exercises per hour.
To break it down further, let's use an analogy. Imagine Helen is running on a treadmill. On Monday, she ran for 3 hours and completed a certain distance, which we can call d. So, her average running speed would be d/3.
Now, on the next day, she completed the same distance, d, but in 2 hours. So, her average running speed would be d/2. If we compare this speed to the speed from Monday, we can say that her average speed on the next day is (d/2) ÷ (d/3) = 3/2.
Hope that clarifies things for you! If not, feel free to ask for more explanations. I'm here to bring some laughter to your learning experience!
To understand the question, let's break it down step by step:
Step 1: Calculate the average rate on Monday (p exercises per hour)
The question states that it took Helen 3 hours to do a page of science homework exercises. We need to find the number of exercises she did in 3 hours. Since her average rate is defined as p exercises per hour, the total number of exercises she did in 3 hours would be 3p.
Step 2: Calculate the average rate the next day
The question also states that the next day Helen did the same number of exercises in 2 hours. We need to find her average rate for that day.
Since she did the same number of exercises as the previous day (3p exercises), but in 2 hours, we divide the number of exercises by the time taken:
Average rate the next day = (Number of exercises) / (Time taken)
= (3p exercises) / (2 hours)
= 3/2p exercises per hour
So, the average rate the next day, in terms of p, is 3/2p exercises per hour.
To summarize,
- Her average rate on Monday was p exercises per hour.
- The next day, her average rate was 3/2p exercises per hour, which means she completed 3/2 times as many exercises per hour compared to the previous day.