# WORD PROBLEMS ON AVERAGE SPEED

## About "Word Problems on Average Speed"

Word Problems on Average Speed :

In this section, we are going to see how word problems on average speed can be solved step by step.

Before look at the word problems on average speed, if you would like to know the basic stuff related to average speed,

## Word Problems on Average Speed

Problem 1 :

David drove for 3 hours at a rate of 50 miles per hour, for 2 hours at 60 miles per hour and for 5 hours at a rate of 70 miles per hour. What was his average speed for the whole journey ?

Step 1 :

Formula for average speed  is

=  Total distance / Total time taken.

And also, formula for the distance is

=  Rate  Time

Step 2 :

Distance covered in the first 3 hours is

=  50  3

=  150 miles

Distance covered in the next 2 hours is

=  60  2

=  120 miles

Distance covered in the last 5 hours is

=  70  5

=  350 miles

Step 3 :

Then, total distance is

=  150 + 120 + 350

=  620 miles

Total time is

=  3 + 2 + 5

=  10 hours

Step 4 :

So, the average speed  is

=  620 / 10

=  62

Hence, the average speed for the whole journey is 62 miles per hour.

Problem 2 :

Jose travels from the place A to place B at a certain speed. When he comes back from place B to place A, his speed is 60 miles per hour.If the average speed for the whole journey is 72 miles per hour, find his speed when he travels from the place A to B.

Step 1 :

Let "a" be the speed from place A to B.

Speed from place B to A  =  60 miles/hour

Step 2 :

Here, both the ways, he covers the same distance.

Then, formula to find average speed is

=  2xy / (x + y)

Step 3 :

x ----> Speed from place A to B

x  =  a

y ----> Speed from place B to A

y  =  60

Step 4 :

Given : Average speed  is 72 miles/hour.

(2 ⋅ ⋅ 60) / (a + 60)  =  72

120a  =  72(a + 60)

120a  =  72a + 4320

48a  =  4320

a  =  90

Hence, the speed from place A to B is 90 miles per hour.

Problem 3 :

David travels from the place A to place B at a certain speed. When he comes back from place B to place A, he increases his speed 2 times. If the constant-speed for the whole journey is 80 miles per hour, find his speed when he travels from the place A to B.

Step 1 :

Let "a" be the speed from place A to B.

Then, speed from place B to A  =  2a

Step 2 :

The distance traveled in both the ways (A to B and B to A) is same.

So, the formula to find average speed is

=  2xy / (x + y)

Step 3 :

x ----> Speed from place A to B

x  =  a

y ----> Speed from place B to A

y  =  2a

Step 4 :

Given : Average speed  =  80 miles/hour

(2 ⋅ ⋅ 2a) / (a + 2a)  =  80

4a² / 3a  =  80

4a / 3  =  80

a  =  60

Hence, the speed from place A to B is 60 miles per hour.

Problem 4 :

A person takes 5 hours to travel from place A to place B at the rate of 40 miles per hour. He comes back from place B to place A with 25% increased speed. Find the average speed for the whole journey.

Step 1 :

Speed ( from A to B )  =  40 miles/hour

Speed ( from B to A )  =  50 miles/hour  (25% increased)

Step 2 :

The distance traveled in both the ways (A to B and B to A) is same.

So, the formula to find average distance is

=  2xy / (x + y)

Step 3 :

x ----> Speed from place A to B

x  =  40

y ----> Speed from place B to A

y  =  50

Step 4 :

Average speed  =  (2 ⋅ 40 ⋅ 50) / (40 + 50)

Average speed  =  44.44

Hence, the average speed for the whole journey is about 44.44 miles/hour.

Problem 5 :

Speed ( A to B )  =  20 miles/hour,

Speed (B to C )  =  15 miles/hour,

Speed (C to D )  =  30 miles/hour

If the distances from A to B, B to C and C to D are equal and it takes 3 hours to travel from A to B, find the average speed from A to D.

Step 1 :

Formula to find distance is

=  Rate  Time

Distance from A to B is

=  20  3

=  60 miles

Given : Distance from A to B, B to C and C to D are equal.

Total distance from A to D is

=  60 + 60 + 60

=  180  miles

Step 2 :

Formula to find time is

=  Distance / Speed

Time (A to B)  =  60 / 20  =  3 hours

Time (B to C)  =  60 / 15  =  4 hours

Time (C to D)  =  60 / 30  =  2 hours

Total time taken from A to D is

=  3 + 4 + 2

=  9 hours

Step 3 :

Formula to find average speed is

=  Total distance / Total time

=  180 / 9

=  20

Hence, the average speed from A to D is 20 miles per hour. To get more problems on average speed,

After having gone through the stuff above, we hope that the students would have understood "Word problems on average speed".

Apart from the stuff given on "Word problems on average speed", if you need any other stuff in this section, 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