Module 11: Rate Problems Flashcards
Distance =
Rate x Time
Time =
Distance / Rate
Rate =
Distance / Time
When I see a rate/time/distance problem, I will
stay organized by setting up a matrix.
X axis always R x T = D. Re-organize later as needed.
RTD problem traps (2)
1) Remember to use AMOUNT OF TIME TRAVELLED, not times of day (if they are provided)
2) Before solving, convert units so they are compatible with others.
Average Speed
Total Distance / Total Time
Expanded:
(D1 + D2) -------------------------- (D1 / R1) + (D2/R2)
(use the T = D/R formula to calculate each time value – IF time not already provided.)
Two Objects rate calculations
Objects moving towards each other: Add the rates
Objects moving away from each other: Add the rates
Objects moving in the same direction at different speeds: Subtract larger rate from smaller rate
Converging Rate problems: Solving for time converged
If they left at the same time, use the same variable T for each rate.
If they left at different times, let the travel time of the object that leaves earlier be represented by T + the difference between their departure times.
Converging Rate problems: Differing speeds (2 scenarios & how to solve)
1) The difference between speeds is given.
- Use different variables for each speed: R for the slow one, and R + X for the fast one (where X is the difference between speeds)
2) Speed given as multiple, percentage, or fraction of another object’s speed.
- Multiple: if Object 1 is x times as fast, 1 = xr, 2 = r
- Percent: If Object 1 is x% as fast, 1 = (x/100)r, 2 = r
Diverging rate question: Total distance traveled?
= to the sum of the distances the two objects have traveled
Round Trip question: how to solve
Set the distance for “to” equal to the distance for “from.” (It’s the same path both ways.) Then, solve for any variables.
Catch-Up Rate question: how to solve 2 scenarios
1) Leave from same spot & catch up to same location:
The distance for both objects will be equal when one catches up to the other. So set R1 * T1 = R2 * T2 and solve for variables.
2) Faster object leaves from X farther away OR faster object must pass slower object by X amount:
Add X to the faster object side of the equation.
If the rate is miles/hour, then units for time must be _____
in hours as well. Using minutes in one & hours in the other gives the wrong answer
“Catch up and pass” problem: quick way to calculate time IF distances are different
Time = Distance delta / Rate delta.
Rate delta: fast rate - slow rate
Distance is _________ to rate and time
Directly proportional
