**Using ratios and rates to solve problems worksheets :**

Worksheets on using ratios and rates to solve problems are much useful to the students who would like to practice problems on ratios and rates.

1. Look at the picture below.

Janet drives from Clarkson to Humbolt in 2 hours. Suppose Janet drives for 10 hours. If she maintains the same driving rate, can she drive more than 600 miles? Justify your answer.

2. In 15 minutes, Lena can finish 2 math problems. At that rate, how many math problems can she finish in 75 minutes ? Use a double number line to find the answer.

3. Anna’s recipe for lemonade calls for 2 cups of lemonade concentrate and 3 cups of water. Bailey’s recipe calls for 3 cups of lemonade concentrate and 5 cups of water. Whose recipe makes stronger lemonade? How do you know ?

4. There are two alloys A and B, both are made up of gold and copper. The ratio between gold and copper in each alloy is given below.

Alloy A (G : C)----> 2 1/3 : 3 1/3

Alloy B (G : C) ----> 3.6 : 4.8

In which alloy do we have more gold ?

**Problem 1 : **

Look at the picture below.

Janet drives from Clarkson to Humbolt in 2 hours. Suppose Janet drives for 10 hours. If she maintains the same driving rate, can she drive more than 600 miles? Justify your answer.

**Solution : **

A double number line is useful, because the regular intervals represent equivalent rates that compare different quantities. The one shown compares the number of miles driven to the time driven for different amounts of time.

She covers 112 miles of distance in 2 hours. Since she maintains the same driving rate, every 2 hours, the distance covered will be increased by 112 miles.

In 8 hours she would have covered 448 miles of distance. After 2 hours, that is in 10 hours, the distance covered will be increased by 112 miles.

So, the distance covered in 10 hours is 560 miles.

It is shown in the picture given below.

**Conclusion : **

From the above working, it is clear that she can not cover more than 600 miles in 10 hours, if she maintains the same driving rate.

**Problem 2 : **

In 15 minutes, Lena can finish 2 math problems. At that rate, how many math problems can she finish in 75 minutes ? Use a double number line to find the answer.

**Solution : **

The one shown compares the number of minutes to the number of math problems.

She finishes 2 math problems in 15 minutes. At this rate, every 15 minutes, the number of math problems finished will be increased by 2.

Let us mark this situation in the above double number line.

Than, we have

From the double number line, it is clear that she can finish 10 math problems in 75 minutes.

**Problem 3 : **

Anna’s recipe for lemonade calls for 2 cups of lemonade concentrate and 3 cups of water. Bailey’s recipe calls for 3 cups of lemonade concentrate and 5 cups of water. Whose recipe makes stronger lemonade? How do you know ?

**Solution :**

**Anna’s recipe : **

2 cups of lemonade and 3 cups of water.

So, the ratio is 2 : 3.

Let us write equivalent ratios to the ratio 2 : 3.

**Bailey’s recipe :**

3 cups of lemonade and 5 cups of water.

So, the ratio is 3 : 5.

Let us write equivalent ratios to the ratio 3 : 5.

Find two columns, one in each table, in which the amount of water is the same. Circle those two columns.

From the circled columns, we get two ratios.

They are,

10 : 15 and 9 : 15

In these two ratios, the second quantity (water) is same.

So, we have to compare the first quantity (Lemonade).

The first quantity (10) in the first ratio is more than the first quantity (9) in the second ratio.

When the quantity of water is same (15) in both recipes, Anna's recipe has more quantity of lemonade concentrate.

Therefore, Anna's recipe has stronger lemonade.

**Problem 4 : **

There are two alloys A and B, both are made up of gold and copper. The ratio between gold and copper in each alloy is given below.

Alloy A (G : C)----> 2 1/3 : 3 1/3

Alloy B (G : C) ----> 3.6 : 4.8

In which alloy do we have more gold ?

**Solution :**

To know the alloy in which we have more gold, we have to compare the given two ratios.

To compare two ratios, both the terms of the ratio must be integers.

Let us convert the terms of the first ratio into integers.

2 1/3 : 3 1/3 = (7/3) : (10/3)

**2 1/3 : 3 1/3 = 7 : 10** ------> multiplied by 3

Let us write equivalent ratios to the ratio 7 : 10

Let us convert the terms of the second ratio into integers.

3.6 : 4.8 = 36 : 48 ------> multiplied by 10

**3.6 : 4.8 = 3 : 4 **------> divided by 12

Let us write equivalent ratios to the ratio 3 : 4

Find two columns, one in each table, in which the the second term is same. Circle those two columns.

From the circled columns, we get two ratios.

They are,

14 : 20 and 15 : 20

In these two ratios, the second quantity (copper) is same.

So, we have to compare the first quantity (gold).

The first quantity (15) in the second ratio is more than the first quantity (14) in the first ratio.

When the quantity of copper is same (20) in both the alloys, Alloy A has more quantity of gold.

Therefore, we have more gold in alloy A.

After having gone through the stuff given above, we hope that the students would have understood "Using ratios and rates to solve problems worksheets".

Apart from the stuff given above, if you want to know more about "Using ratios and rates to solve problems worksheets", please click here

Apart from "Using ratios and rates to solve problems worksheets", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**