Rate Flashcards
Rate question ask
- how far
- how fast
- how long
Distance
Rate*Time
** and you can derive the rate and time equation from the equation above
Matrix of Rate-Time Distance Problems
Rate * Time = distance
Object Travelling
Average Rate
Total Distance D1+D2
———————- = ———-
Total Time T1+T2
*same object
When two object converge (meet)
The total distance will be equal to the sum of the individuals distance each object travels
= Total distance of object 1 +object 2 = distance object 1 + distance object 2
e.g: For example, two-car were 100 miles apart and traveling toward each other at a constant rate, when they meet the total distance the two cars travel, regardless of how fast each travels or where they meet, will equal 100 miles. It doesn’t matter whether one car travels 99.9 miles and the other car travels 0.1 miles. Together they must travel 100 miles.
When both objects leave at the same time of day and converge at constant rates
they will have traveled for the same time at the instant that they meet
when two objects leave at different times and converge at a constant rate, the travel time of the object that leaves later can be represented by some variable t; the travel time of the object that leaves earlier can be represented by t+ the difference between their departure times
t; the travel time of the object that leaves earlier can be represented by t+ the difference between their departure times.
- Remember, we always add to the object leaving first because the total travel time will be greater for that object
When one object is traveling faster than another object
consider letting the slower object’s speed be some variable r and the faster object’s speed be r+ the difference in speeds
When the first object is x times as fast as the second object,
let the rate of the second object be r and the rate of the first object be xr. When the first object is x percent as fast as the second object, let the rate of the second object be r and let the rate of the first object be (x/100)r
In a diverging questions, if two objects start at the same place and move in opposite directions,
then the sum of the distances that two objects must equal the total distance traveled between the two objects
* Distance Total= Distance object 1 + Distance object 2
In a round trip problem, the distance an object travels from the starting point to the destinatiion
equals the distance the object travels back from the destination to the stating point
In a round trip when only the total time traveled is provided
consider letting the time to a destination equal some variable t and the time back equal (total trip time -t)
Catch up rates questions
the speed differential between two objects allows the faster object to catch up the slower object
When two objects start from the same point and catch up to each other
both objects will have traveled the same distance when they meet
Catch up and pass rate questions
The faster object distance is equal to the slower object distance plus any difference in starting points and any distance by which the faster object must pass the slower object
The time that it will take a faster object to “catch up” and pass” a slower object can be determined by
change in rate
*The change in distance is simply the extra distance that the faster object must travel over that of the slower object. The change in rate is simply (the rate of the faster object)- (the rate of the slower object )
Relative motion questions
an object travels relatively faster when it is moving along with an outside force than when it is traveling under its own power. Conversely, an object will move relatively slower when it is moving against an outside force than when its is moving under its own power
If/ then rate questions
if [object] had traveled [some rate], it would have [saved/added] t hours to its time
e.g If Jean had driven at 55 mph, she would have arrived at her destination 2 hours later than she did
Time Zone Rate time
when solving a rate time distance problem with time-zone changes, convert the time zone of the destination to the time zone of the origin to accurately compute the time traveled.
Rates is a ratio that compares two quantities of
two different units of measurements
Distance
Rate*Time
Distance is directly proportional to rate and time
If rate increases and time remains constant, then distance must increase; if time increases and rate remains constant then the distance must increase. Distance is therefore directly proportional to both rate and time
Rate is inversely proportional to time and directly proportional to distance
If the rate at which an object travels a certain distance increases, the time it takes to travel the distance decreases, and vice versa
Travel Time is inversely proportional to rate and directly proportional to distance.
As the distance that an object must travel at a certain speed increases, the time to travel that distance also increases, and vice versa
