Chapter 9: Rate Problems

fuel efficiency is a type of rate that shows the relationship between…

the distance a vehicle travels and the volume of fuel it burns to do so

fuel efficiency=

distance traveled/volume of fuel consumed

if a motorcycle burns 5 liters of gas to travel 310 kilometers, then what is the motorcycle’s fuel efficiency in kilometers per liter?

fuel efficiency = 310 kilometers/5 liters = 62 kilometers/liter

in the matrix, each column corresponds to one of the variables in the rate-time-distance formula and each row represents an object traveling, what is the formula?

rate x time = distance

if a jet flew 500 miles per hour for 4 hours, what is the jet’s total travel distance?

500 miles/hour x 4 hours= 2000 miles

before you fill in the cells in the matrix , make sure that the units of measurement are

compatible

time =

distance / rate

rate =

distance / time

average rate =

total distance / total time

converging rate questions

two objects are moving toward each other. when two objects converge (meet), the total distance will be equal to the sum of the individual distances each object travels

when two objects converge at a constant rate and meet, the total distance the object cover is defined by the equation:

distance_{object 1} + distance_{object 2} = distance_total

when two objects leave at different times and converge at a constant rate, how are the times represented?

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 + difference between their departures

when one object is traveling faster than another object, how do you represent the different speeds?

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

when one object is relatively faster than another object, how do you represent the different rate?

let r= the rate of the second object and the rate of the first object be xr

when two objects move away from each other, the total distance that the two objects cover is represented by what equation

distance_{object 1} + distance_{object 2}= distance_total

true or false: the same “total distance” formula is used in both converging and diverging rate questions

true

what is the equation we generally use in round-trip rate questions?

distance₁ = distance ₂

when the total time traveled is provided in round-trip rate questions, how do you set up the equation

travel time to destination = t
travel time back = (total travel time - t)

how would you solve this problem: a jet flies from town X to town Y at a constant speed of 675mph, then immediately returns along the same route at a constant speed of 450mph. if the round trip takes 5 hours, how long does the return trip take?

from x to y —> 675t

from y to x —> 450(5 - t)

675t = 450(5-t)

1,125t = 2,250

t = 2,250/1,125 = 2

5 - 2 = 3 hours

in round trip problems, the distance traveled from the starting point to the destination equals

the distance from the destination back to the starting point

in catch-up problems, two travelers leave from the same location at different times, with the ______ traveler leaving first

slower

how do you set up catch-up rate questions?

distance _{traveler 1} = distance_{traveler 2}

in catch up problems, when the catch up occurs, both objects will have traveled the same __________

distance

Al leaves his house and walks west at a constant rate of 3 miles per hour. Two hours later, Gal leaves the same house and walks west at a constant rate of 4 miles per hour. how long will it take Gal to catch up to Al

Al = 3(t+2) = (3t+6)

Gal = 4t - 4t

4t = 3t+6

t= 6 hours

how do you set up the equation for catch-up and pass rate questions?

Distance _{faster traveler} = Distance _{slower traveler} + Distance _additional

Harry and Sally start driving east from the same location at the same time. If Harry’s rate is 50mph and Sally’s rate is 60mph, how many hours will it take Sally to be 35 miles ahead of Harry?

Harry = 50t

Sally = 60t

60t = 50t + 35

in all catch-up and pass problems, the two travelers have identical

travel times

distance =

rate x time

in relative motion problems, an outside force acts on an object to change its relative _______

speed

an object travels relatively ________ when it is moving WITH an outside force than when it travels naturally only under its power

faster

an object travels relatively ________ when it is moving AGAINST an outside retarding force than when it travels naturally only under its own power

slower

when calculating relative speeds, make sure the speeds are expressed in the same units of

measurement

how do you solve relative motion rate questions? (using 200mph and wind)

set up the time with an outside force acting on it and an outside forcing acting against it, find the times and set them equal to each other

200+x

200-x