# EXPLORING RATES

Exploring rates :

Commonly used rates like miles per hour make it easy to understand and compare rates.

## Exploring rates - Example

Example 1 :

Jeff hikes 1/2 mile every 15 minutes, or 1/4 hour. How far does he hike in 1 hour ?

Solution :

We can use proportion to solve this problem.

Let "a" be the number of miles covered by Jeff in 1 hour.

Then, we have

1/2 : 1/4  =  a : 1

1 x 1/2  =  (1/4)a

1/2  =  a/4

2  =  a

Hence, Jeff hikes 2 miles in 1 hour.

Examples 2 :

At a summer camp, the campers are divided into groups. Each group has 16 campers and 2 cabins. How many cabins are needed for 112 campers ?

Solution :

First we have to find how many campers can accommodate in one cabin.

To find the number of campers accommodated in 1 cabin, we have to divide 16 by 2.

16/2  =  8

8 campers can accommodate in 1 cabin.

To find the number of cabins required for 112 campers, we have to divide 112 by 8.

112 / 8  =  14

Hence, 14 cabins needed for 112 campers.

Examples 3 :

If 350 miles of distance covered 7 hours, find the distance covered by 6 hours ?

Solution :

First we have to find how many miles of distance covered in 1 hour.

To find the distance covered in 1 hour, we have to divide 350 by 7.

350/7  =  50

In 1 hours, 50 miles of distance covered.

In 6 hours, the distance covered  =  6 x 50  =  300 miles.

Examples 4 :

Petra jogs 3 miles in 27 minutes. Find the unit rate in minutes per mile. How long would it take her to jog 5 miles ?

Solution :

To find the unit rate in minutes per mile, we have to divide 27 minutes by 3 miles.

27 ÷ 3  =  27/3  =  9

Unit rate in minutes per mile  =  9

That is, it takes 9 minutes to cover 1 mile of distance.

To find the time taken to cover 5 miles, we have to multiply 5 and 9

5 x 9  =  45

Therefore, it will take 45 minutes to cover 5 miles of distance.

After having gone through the stuff given above, we hope that the students would have understood "Unit rates".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6