Question

a bus covers a certain distance in 42 minutes if it runs at a speed of 50 km\hr what must be the speed of the bus in order to reduce the time of the jorneyto 30 minutes​

Answer 1

GIVEN :–

• A bus covers a certain distance in 42 minutes if it runs at a speed of 50 km/hr.

TO FIND :–

• What must be the speed of the bus in order to reduce the time of the journey to 30 minutes ?

SOLUTION :–

• Time = 42 min = 42 × 60 = 2520 sec

• Speed = 50 km/hr = 50 × 5/18 = 125/9 m/sec

• We know that –

$\\ \large \implies{ \boxed{ \bf Speed \: = \dfrac{Distance}{Time}}}$

• Now put the values –

$\\\implies\bf \dfrac{125}{9} \: = \dfrac{Distance}{2520}$

$\\\implies\bf Distance = \dfrac{125}{9} \times 2520$

$\\\implies\bf Distance =125 \times 280$

$\\\implies \large{ \boxed{\bf Distance =35000 \: \: m}}$

• New speed –

• When T = 30 min , T = 1800 sec

$\\\implies\bf Speed \: = \dfrac{35000}{1800}$

$\\\implies\bf Speed \: = \dfrac{350}{18}$

$\\\implies\bf Speed \: = \dfrac{175}{9}$

$\\\implies\bf Speed \: = \dfrac{175}{9} \:m/sec$

$\\\implies\bf Speed \: = \dfrac{175}{9} \times \dfrac{18}{5} \:km/hr$

$\\\implies\bf Speed \: = \dfrac{175 \times 2}{5}\:km/hr$

$\\\implies\bf Speed \: = \dfrac{350}{5}\:km/hr$

$\\\implies \large{ \boxed{\bf Speed \: = 70 \:\:km/hr }}$

Answer 2

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: AnSwer :- \: \star}}}}}$

A bus covers a certain distance in 42 minutes if it runs at a speed of 50 km\hr what must be the speed of the bus in order to reduce the time of the journey to 30 minutes.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\large{ \boxed{\bf Speed \: = 70 \:\:km/hr }}$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

❥ Speed = 50km/hr { Converting into metre per second }

= 50 × 5/18

= 125/9m/sec

❥ Time = 42 minutes { Converting into seconds }

= 42 × 60 = 2520 sec

$\Large{\underline{\underline{\bf{Find:-}}}}$

❥ Speed of the bus ?

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Here we go !

❥ In order to solve the Question

Required formula :-

$\\ \large { \boxed{ \bf Speed \: = \dfrac{Distance}{Time}}}$

Now as per the given :-

$\bf \dfrac{125}{9} \: = \dfrac{Distance}{2520}$

$\\bf Distance = \dfrac{125}{9} \times 2520$

$\\bf Distance =125 \times 280$

$\large{ \boxed{\bf Distance =35000 \: \: m}}$

As now the New speed

$\bf Speed \: = \dfrac{35000}{1800}$

$\bf Speed \: = \dfrac{350}{18}$

$\bf Speed \: = \dfrac{175}{9}$

$\bf Speed \: = \dfrac{175}{9} \:m/sec$

$\bf Speed \: = \dfrac{175}{9} \times \dfrac{18}{5} \:km/hr$

$\bf Speed \: = \dfrac{175 \times 2}{5}\:km/hr$

$\bf Speed \: = \dfrac{350}{5}\:km/hr$

${\bf Speed \: = 70 \:\:km/hr }}$

Additional Information :-

✮ What is speed ?

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time.

Note :-

An object with no movement at all has a zero speed.

✮ What is distance ?

Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.

✮ What is speed - distance formula ?

❥The formula speed = distance ÷ time can be rearranged, just like any other equation.

❥ The formula can be rearranged in three ways: speed = distance ÷ time. distance ↠ speed × time.