Rate

Question 1

Rate question ask

Answer 1

• how far
• how fast
• how long

Question 2

Distance

Answer 2

Rate*Time

** and you can derive the rate and time equation from the equation above

Question 3

Matrix of Rate-Time Distance Problems

Answer 3

Rate * Time = distance

Object Travelling

Question 4

Average Rate

Answer 4

Total Distance D1+D2
———————- = ———-
Total Time T1+T2

*same object

Question 5

When two object converge (meet)

Answer 5

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.

Question 6

When both objects leave at the same time of day and converge at constant rates

Answer 6

they will have traveled for the same time at the instant that they meet

Question 7

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

Answer 7

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

Question 8

When one object is traveling faster than another object

Answer 8

consider letting the slower object’s speed be some variable r and the faster object’s speed be r+ the difference in speeds

Question 9

When the first object is x times as fast as the second object,

Answer 9

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

Question 10

In a diverging questions, if two objects start at the same place and move in opposite directions,

Answer 10

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

Question 11

In a round trip problem, the distance an object travels from the starting point to the destinatiion

Answer 11

equals the distance the object travels back from the destination to the stating point

Question 12

In a round trip when only the total time traveled is provided

Answer 12

consider letting the time to a destination equal some variable t and the time back equal (total trip time -t)

Question 13

Catch up rates questions

Answer 13

the speed differential between two objects allows the faster object to catch up the slower object

Question 14

When two objects start from the same point and catch up to each other

Answer 14

both objects will have traveled the same distance when they meet

Question 15

Catch up and pass rate questions

Answer 15

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

Question 16

The time that it will take a faster object to “catch up” and pass” a slower object can be determined by

Answer 16

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 )

Question 17

Relative motion questions

Answer 17

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

Question 18

If/ then rate questions

Answer 18

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

Question 19

Time Zone Rate time

Answer 19

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.

Question 20

Rates is a ratio that compares two quantities of

Answer 20

two different units of measurements

Question 21

Distance

Answer 21

Rate*Time

Question 22

Distance is directly proportional to rate and time

Answer 22

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

Question 23

Rate is inversely proportional to time and directly proportional to distance

Answer 23

If the rate at which an object travels a certain distance increases, the time it takes to travel the distance decreases, and vice versa

Question 24

Travel Time is inversely proportional to rate and directly proportional to distance.

Answer 24

As the distance that an object must travel at a certain speed increases, the time to travel that distance also increases, and vice versa