Question

3. A train travels 40 km at
a uniform
speed of 30 km/hr. it's average speed after travelling another 40km is 45 km/hr for the whole journey. its speed in the second half of the journey is?
​

Answer 1

GIVEN :–

• A train travels 40 km at a uniform speed of 30 km/hr.

• It's average speed after travelling another 40km is 45 km/hr for the whole journey.

TO FIND :–

• It's speed in the second half of the journey is = ?

SOLUTION :–

• Time taken in first 40 km is –

$\\ \implies { \bold{ T_{1} = \dfrac{Distance}{Speed} }}$

$\\ \implies { \bold{ T_{1} = \dfrac{40}{30} }}$

$\\ \implies { \bold{ T_{1} = \dfrac{4}{3} }}$

• Time taken in next 40 km is (Let speed is 'x' ) –

$\\ \implies { \bold{ T_{2} = \dfrac{Distance}{Speed} }}$

$\\ \implies { \bold{ T_{2} = \dfrac{40}{x} }}$

$\\ \: \: \: { \huge{.}} \: \: \: \: { \bold{Total \: \: time = T_{1} + T_{2} = \dfrac{40}{x} + \dfrac{4}{3} }}$

$\\ \: \: \: { \huge{.}} \: \: \: \: { \bold{Total \: \: distance = 40 + 40 = 80km}}$

$\\ \implies { \bold{Average \: \: speed = \dfrac{Total \: \: distance}{Total \: \: time} }}$

$\\ \implies { \bold{45 = \dfrac{80}{ \dfrac{40}{x} + \dfrac{40}{30} } }}$

$\\ \implies { \bold{45 = \dfrac{2}{ \left(\dfrac{1}{x} + \dfrac{1}{30} \right) } }}$

$\\ \implies { \bold{45 = \dfrac{2}{ \left(\dfrac{30 + x}{30x}\right) } }}$

$\\ \implies { \bold{45 = \dfrac{2(30x)}{30 + x} }}$

$\\ \implies { \bold{45(30 + x)= 60x}}$

$\\ \implies { \bold{45 \times 30 + 45x= 60x}}$

$\\ \implies { \bold{1350= 60x - 45x}}$

$\\ \implies { \bold{1350= 15x}}$

$\\ \implies { \bold{x = \cancel\dfrac{1350}{15} }}$

$\\ \implies \large{ \boxed { \bold{x = 90 \: \: \dfrac{km}{hr} }}}$

• Speed in second half of the journey is 90 km/hr

Answer 2

Answer:

Hello mate ✌️

Explanation:

ATQ

45km/h=40+40/ 40/30+40/x

45=80/4/3+40/x

45=80/4x+120/3x

45=80×3x/4x+120

45=240x/4x+120

45(4x+120)=240x

180x+5400=240x

5400=240x-180x

5400=60x

5400/60=x

90=x

speed for next half of journey =90km/h

hope it will be helpful to you ✌️

@:-)

itz Essar 03 ❤️