Question

1)A boy covers the distance of 25 km in 4 hours partly on foot and the rate of 3.5kmph and partly on cycle at 9 kmph . find the distance covered on.
2)Punnet starts from his house to school on cycle at 10 kmph and reaches 4 minutes earlier than the scheduled time. however, if he cycles at 8 kmph he is late by 5 minutes. what what is the distance between his residence and the school?
3) A steamer goes downstream and covers the distance between two ports in 4 hours while it covers the same distance upstream in 5 hours if the speed of the steam is tu 2 kilometre per hour. find the speed of the steamer in still water.
4) the difference between the squares of the consecutive numbers is 95 find the numbers?

pls Answer correctly​

Answer 1

Answer:-

1) Let the distance covered on foot be x km.

Then, the distance covered on bicycle =(25 -x)km.

Time taken to cover x km at 3.5kmph

= ( x/3.5)hrs

Time taken to cover ( 25 - x ) km at 9 kmph

$= \bigg( \dfrac{25 - x}{9}\bigg)hours$

$\therefore \dfrac{x}{3.5} + \dfrac{25 - x}{9} = 4$

$\implies \dfrac{2x}{7} + \dfrac{25 - x}{9} = 4$

$\implies18x + 7(25 - x) = 252$

( multiplying throughout by 63 )

$\implies11x = (252 - 175) = 77$

$\implies \: x = 7$

Answer:- Hence, Distance covered on foot = 7 km.

2) Let the required distance be x km.

Time taken to cover x km at 10kmph =

( x/10 ) hrs

Time taken to cover x km at 8kmph =

( x/8 ) hrs

Difference in the two times taken

= 9 mins

= ( 9/60 )hour

$\therefore \dfrac{x}{8} - \dfrac{x}{10} = \dfrac{9}{60}$

( multiplying throughout by 120 )

$\implies 15x - 12x = 18$

$\implies 3x = 18$

$\implies x = 6$

Answer:- Hence, Distance between the residence and school is 6km.

3) Let the speed of the steamer in still water be

x km/hr.

Then, speed downstream

= ( x + 2 ) km/hr

Speed upstream

= ( x - 2 ) km/hr

Distance covered in 4 hours at ( x + 2 ) km/hr

= 4 ( x + 2 ) km

Distance covered in 5 hours at ( x - 2 ) km/hr

= 5 ( x - 2 ) km.

∴ 4( x + 2 ) = 5( x - 2 )

⟹ 4x + 8 = 5x - 10

⟹ 5x - 4x = 8 + 10

⟹ x = 18

Answer:- Hence, Speed of the steamer in still water is 18km/hr.

4) Let the two consecutive numbers be x and x +1

A.T.Q

( x + 1 )² - x = 95

⟹ ( x² + 2x + 1 ) - x² = 95

⟹ 2x + 1 = 95

⟹ 2x = 95 - 1

⟹ 2x = 94

⟹ x = 47

1st number = 47

2nd number

= x + 1

= 47 + 1

= 48

Answer:- Hence, the numbers are 47 and 48.

Key Concepts

1) What is an equation ??

Ans) A statement of equality of two algebraic expressions involving one or more variables is called an equation.

2) What is transposition ??

Ans) Any term of an equation may be taken to the other side with the sign changed. This process is called transposition.

Answer 2

Step-by-step explanation:

hope it will help you thank you