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Difference between two rate questions!

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Junior | Next Rank: 30 Posts
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by Codebreaker2k » Tue Feb 05, 2013 4:43 pm
Question 1:

If Eileen drives at an average speed of 50 miles per hour for 3 hours and an average speed of 60 miles per hour for the next 2 hours, what is her average speed for the entire trip?

Answer: 3(50)=150, 60(2)=120 so (150+120)/5=54

Question 2:

A train travels at a speed of 60 mph for the first 180 miles of its trip, then it travels at a speed of 45 mph for the remaining 180 miles of its trip. What is the train's average speed for the entire trip?

Answer: 180/60=3, 180/45=4 so (180+180)/(4+3)=51 and 3/7.


MY QUESTION: In the first question we used multiplication initially, and in the second we used division first. How does one differentiate when to multiply or divide initially? I want to make sure I am translating the question correctly.

Thank you!
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by vkb001 » Tue Feb 05, 2013 4:56 pm
a. Average speed is total distance travelled, divided by total time taken to travel that total distance.
b. Distance = Speed * Time

In Question 1:
To find average speed, you have total time given. You need total distance travelled. Therefore, you use formula (b), where you MULTIPLY speed and time, to get the distance and formula (a) to find average speed.

In Question 2:
Here, you have speed and distance given. You need total time. To get time, you need to DIVIDE distance by speed. And given this new information, calculate average speed.

Some unsolicited advice: I'd suggest you remember the concept and not when to multiply and divide. That way, even if there's a curved-ball thrown at you, you'd be able to answer it easily in the exam.
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by ceilidh.erickson » Thu Feb 07, 2013 11:48 am
vkb001 is absolutely right! Don't try to memorize which situations require multiplication and which require division. Think about the relationship between rate (speed), time, and distance: R*T=D. I recommend writing down that formula whenever you see a rate problem, then ask yourself - which pieces do I have?

One simple way to keep this all organized is to use a rate chart. This will make it easy to see when you multiply and when you divide. For the first question:

Image

The chart can help you see that what's missing is the distance for each leg of the journey. Multiply the rate by the time to find these. Average speed = (total distance)/(total time), so calculate: average speed = 54.

Second problem:
Image

For the second problem, the chart helps you to see that the missing information is the time. Divide each distance by the respective rate to find the time. The add up your total distance, your total time, and divide: average speed = 360/7.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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