# ACT Math : How to find rate

## Example Questions

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### Example Question #21 : Proportion / Ratio / Rate

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?

Explanation:

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

.

### Example Question #22 : 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.

Explanation:

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 #23 : 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.

Explanation:

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 #31 : Proportion / Ratio / Rate

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.

Explanation:

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 #32 : Proportion / Ratio / Rate

Twenty bakers make  dozen cookies in eight hours.  How many cookies does each baker make in an hour?

Explanation:

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 #33 : Proportion / Ratio / Rate

If it takes  workers  hours to make  widgets, how many hours will it take for  to make  widgets?

Explanation:

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.

Explanation:

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 .

### Example Question #35 : Proportion / Ratio / Rate

A climber scrambles over  yards of rocks in  minutes and then returns across the rocks.  If his total rate was  yards per minute, how long did it take him to return back?

Explanation:

Begin by setting up the standard equation

However, for our data, we know the distance and the rate only.  We do not know the time that it took for the person's return.  It is , where  is the return time.  Thus, we can write:

Solving for , we get:

, which rounds to  minutes.

### Example Question #36 : Proportion / Ratio / Rate

Columbus is located  away from Cincinnati.  You drive at  for the first .  Then, you hit traffic, and drive the remaining portion of the way at only .  How many minutes did it take you to reach your destination?

Explanation:

Here, we need to do some unit conversions, knowing that there are  in an .  We have two different rates, which result in two different equations, which we need to add to get a total time.

.

### Example Question #37 : Proportion / Ratio / Rate

Max drives his car at a constant rate of 25 miles per hour. At this rate, many minutes will it take him to drive 15 miles?

32

28

36

20

40

36

Explanation:

We know that it takes Max an hour to drive 25 miles. We also know that there are 60 minutes in an hour. Using this information we can create the following ratio:

We are trying to calculate the the amount of time it will take to drive 15 miles. Let's create a proportion and use a variable for the unknown time.

Cross-multiply and solve for the time.

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