All ACT Math Resources
Example Questions
Example Question #3 : How To Find Rate
A new car can travel an average of 63 miles per gallon of gasoline. Gasoline costs $5.05 per gallon. How much would it cost to travel 6,363 miles in this car?
$510.05
$505
$101
$510
$405.05
$510.05
First, find the total amount of gas necessary for the trip. 6363/63 = 101 gallons (easy to see as 63 * 100 = 6300 + 1 * 63 = 6363). Then multiply the number of gallons by the price per gallon of gasoline, 5.05 * 101 = $510.05 and is your answer (again, easy to see when 5.05 * 100 + 1 * 5.05).
Example Question #4 : How To Find Rate
If Denise drives at a constant rate of 65 mph for 15 hours, how far will she drive in miles?
Remember that distance/time=rate, so then:
x/15 = 65
x = 65 * 15
x = 975 miles
Example Question #71 : Fractions
Joe and Jake canoed down stream in 30 minutes and then up stream in 60 minutes. How fast were they paddling if the river current is 3 mph?
3 mph
7 mph
9 mph
None of the answers are correct
5 mph
9 mph
The general equation is distance = rate x time. In addition, the distance upstream is the same as the distance downstream. So, rup x tup = rdown x tdown. Be sure to convert minutes to hours because the rate is given in mph (miles per hour).
Therefore, (r + 3)(1/2) = (r – 3)(1) and solve for r.
Note, r + 3 is the downstream rate and r – 3 is the upstream rate
Example Question #72 : Fractions
A car gets 34 mpg on the highway and 28 mpg in the city. If Sarah drives 187 miles on the highway and 21 miles in the city to get to her destination, how many gallons of gas does she use?
In order to get the total amount of gas used in Sarah’s trip, first find how much gas was used on the highway and add it to the amount used in the city. Highway gas usage can be found by dividing
and city usage can be found by dividing
.
Then we add these two answers together and get
Example Question #28 : Proportion / Ratio / Rate
A car travels for three hours at then for four hours at
, then, finally, for two hours at
. What was the average speed of this care for the whole trip? Round to the nearest hundredth.
We know that the rate of a car can be written in the equation:
This means that you need the distance and time of your total trip. We know that the trip was a total of or
hours. The distance is easily calculated by multiplying each respective rate by its number of hours, thus, you know:
Therefore, you know that the rate of the total trip was:
Example Question #24 : Proportion / Ratio / Rate
A container of water holds and is emptied in fifteen days time. If no water added to the container during this period, what is the rate of emptying in
? Round to the nearest hundredth.
Recall that the basic form for a rate is:
, where
is generically the amount of work done. Since the question asks for the answer in gallons per hour, you should start by changing your time amount into hours. This is done by multiplying
by
to get
.
Thus, we know:
Example Question #1461 : Act Math
A large reservoir, holding
, has an emptying pipe that allows out
. If an additional such pipe is added to the reservoir, how many gallons will be left in the reservoir after three days of drainage occurs, presuming that there is no overall change in water due to addition or evaporation.
The rate of draining is once the new pipe is added. Recall that:
, where
is the total work output. For our data, this means the total amount of water. Now, we are measuring our rate in hours, so we should translate the three days' time into hours. This is easily done:
Now, based on this, we can set up the equation:
Now, this means that there will be or
gallons in the reservoir after three days.
Example Question #31 : Proportion / Ratio / Rate
Twenty bakers make dozen cookies in eight hours. How many cookies does each baker make in an hour?
This problem is a variation on the standard equation . The
variable contains all twenty bakers, however, instead of just one. Still, let's start by substituting in our data:
Solving for , we get
.
Now, this represents how many dozen cookies the whole group of make per hour. We can find the individual rate by dividing
by
, which gives us
. Notice, however, that the question asks for the number of cookies—not the number of dozens. Therefore, you need to multiply
by
, which gives you
.
Example Question #1462 : Act Math
If it takes workers
hours to make
widgets, how many hours will it take for
to make
widgets?
This problem is a variation on the standard equation . The
variable contains all the workers. Therefore, we could rewrite this as
, where
is the number of workers and
is the individual rate of work. Thus, for our first bit of data, we know:
Solving for , you get
Now, for the actual question, we can fill out the complete equation based on this data:
Solving for , you get
.
Example Question #34 : Proportion / Ratio / Rate
At the beginning of a race, a person's speed is miles per hour. One hour into the race, a person increases his speed by
. A half an hour later, he increases again by another
. If he finishes this race in two hours, what is the average speed for the entire race? Round to the nearest hundredth of a mile per hour.
Recall that in general
Now, let's gather our three rates:
Rate 1:
Rate 2:
Rate 3:
Now, we know that the time is a total of hours. Based on our data, we can write:
This is miles per hour, which rounds to
.
Certified Tutor
All ACT Math Resources
