**Problem 1 :**

Two water taps together can fill a tank is 9 ⅜ hours. The tap of the larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

**Solution :**

Let 'x' be the time taken by the smaller pipe to fill the part of tank.

Then, time taken by the larger pipe to fill the part of the tank is (x - 10).

Total time taken by two pipes = 9 3/8

part of tank filled by the smaller pipe in 1 hour = 1/x

part of tank filled by the larger pipe in 1 hour = 1/(x-10)

[1/x] + [1/(x - 10)] = 1/(9 3/8)

[1/x] + [1/(x - 10)] = 8/75

[(x - 10 + x)] / [x(x -10)] = 8/75

(2x - 10)/(x^{2} - 10 x) = 8/75

75(2x - 10) = 8(x^{2} - 10x)

150x - 750 = 8x^{2} - 80x

8x^{2} - 80x - 150x + 750 = 0

8x^{2} - 230x + 750 = 0

8x^{2} - 200x + 30x + 750 = 0

8x(x - 25) + 30(x - 25) = 0

(8x + 30) (x - 25) = 0

8x + 30 = 0 or x - 25 = 0

x = -15/4 or x = 25

Because x represents amount of time, it can not take negative value.

Then,

x = 25

So, time taken by smaller pipe alone to fill the tank is 25 hours.

Time taken by larger pipe alone to fill the tank is

= 25 - 10

= 15 hours

**Problem 2 :**

A express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of the two trains.

**Solution :**

Let 'x' be the average speed of passenger train.

Then, the average speed of express train is (x + 11).

Distance to be covered = 132 km

Time = Distance/speed

T_{1} = 132/x

T_{2} = 132/(x + 11)

[132/x] - [132/(x + 11)] = 1

132[(1/x) - (1/(x + 11))] = 1

132 [ (x + 11 - x)/(x(x + 11))] = 1

132[11/(x^{2} + 11x)] = 1

1452/(x^{2} + 11x) = 1

1452 = x^{2} + 11x

x^{2} + 11x - 1452 = 0

x^{2} + 44x - 33x -1452 = 0

x(x + 44) - 33(x + 44) = 0

(x + 44) (x - 33) = 0

x = -44 or x = 33

Because x represents the average speed, it can not take negative value.

Then,

x = 33

So, the average speed of passenger train is 33 km/hr.

Average speed of express train is

= x + 11

= 33 + 11

= 44 km/hr

**Problem 3 :**

Sum of area of two squares is 468 m². If the difference of their perimeter is 24 m,find the sides of the two squares.

**Solution :**

Let 'x' be the side length of one square

let 'y' be the side length of another square

Sum of area of two squares = 468

x^{2} + y^{2} = 468 -----(1)

4x - 4y = 24

4x = 24 + 4y

x = (24 + 4y)/4

x = 6 + y -----(2)

Substitute x = 6 + y in (1).

(1)-----> (6 + y)^{2} + y^{2} = 468

6^{2} + 2(6)y + y^{2} + y^{2} = 468

36 + 12y + 2y^{2} = 468

2y^{2} + 12y - 468 + 36 = 0

2y^{2} + 12y - 432 = 0

Divide the whole equation by 2.

y^{2} + 6 y - 216 = 0

y^{2} + 18y - 12y - 216 = 0

y(y + 18) - 12(y + 18) = 0

(y - 12) (y + 18) = 0

y - 12 = 0 or y + 18 = 0

y = 12 or y = - 18

Because y represents the length, it can not take negative value. .

Then,

y = 12

Substitute 12 for y in (2).

(2)-----> x = 6 + 12

x = 18

So, the side length of two squares are 18 cm and 12 cm.

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

HTML Comment Box is loading comments...

You can also visit the 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**

**Trigonometry 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**