Rate Problems Flashcards
rate*time = ?
distance
average rate =?
total distance/total time = (d1+d2)/(t1+t2) if there is a two part trip
if object traveling is going from point A to point B and back along the same path, d1=d2
for an average rate problem where you are given the rates of the two legs of the trip and that the two legs of the trip are equal distances, but not what the actual distance is, what are the two ways to still find the average rate?
- set each distance equal to d (they will cancel out leaving you with a scalar value at the end)
- FASTER WAY: let distance be a value that is a multiple of both the rates (preferably the LCM)
what is known about distance in a convergence problem
the total distance traveled is the sum of the distances traveled by each object
true or false: in a convergence rate problem, if both objects leave at the same time, they will have been travelling for the same amount of time when they meet?
true
for rate problems where objects leave at different times, how do we assign the time variable to each object?
the object that leaves later travels for time t, and the object that leaves first travels for t+(the amount of time it left before the other object)
for rate problems where one object travels faster than the other object, how do we assign the rate variables to each object?
slower object: r
fast object: r+difference in rates
for rate problems where one object travels relatively faster than another object (ex: object one travels twice as fast as object two), how do we assign the rate variables to each object
baseline object: r
scaled object: xr, where x is the factor by which it is faster or slower
ex: car A is 50% as fast as car B -> rate(a) = 50/100*r, and rate(b)=r
how would rates be expressed in the following example:
car A is 50% as fast as car B
rate B: r
rate A: (50/100)*r
for round trip problems, an object travels to a destination along a given path and returns to its starting point along the exact same path. In this type of problem what is the relationship between the distances of the two legs of the trip?
d1 = d2
for a round trip problem where only the total time is provided, what is a way to express the two legs of the trip given only the total time?
Suppose the total time given is 10 hours. Let the first leg of the trip be t hours. Then the second leg is 10-t hours.
for catch up problems where the two objects start at the same point, by the time the faster object catches up to the slower object what is true about their distances
they are equal
for catch up problems where the two objects start at the same point, by the time the faster object catches up to the slower object what is true about their travel times?
the slower object’s travel time is greater than the faster object’s travel time
for a catch up and pass rate problem, what adjustment do we make to the faster objects distance traveled?
distance traveled of faster object = distance of slower object + additional distance traveled
shortcut formula for time it takes a faster object to catch up and pass a slower object: ?
time = (change in distance)/(change in rate); where change in distance is how much further the faster object must travel, and change in rate is how much faster the faster object travels than the slower object
what are catch up and wait problems?
a faster object passes a slower object, and after traveling at their respective rates for some time, the faster object stops and waits for the slower object to catch up
what is unique about the travel times and distances in catch up and wait problems where the two objects begin their journey at the same point?
travel times are different, and travel distances are the same
distance is (directly/inversely) proportional to both rate and time?
directly
rate is (directly/inversely) proportional to time and (directly/inversely) proportional to distance?
inversely, and directly
time is (directly/inversely) proportional to rate and (directly/inversely) proportional to distance?
inversely, and directly
determining whether a rate, time, or distance meets an inequality with data sufficiency questions
Q: If it took Quinn 4.5 hours to drive from point a to point b, did quinn travel less than 270 miles?
1) his average speed for the trip was less than 55 mph
2) his average speed for the trip was greater than 45 mph
*see screenshot for process
data sufficiency inequality MORE stuff
*see screenshot for intro to problem
see screenshot for rest of problem
fuel efficiency is a rate, so how does this play into rate*time=distance
fuel efficiency * volume of fuel consumed = distance traveled
rate * volume = distance
