Question

b On a 400km track, a train travels the first 250 km at a uniform speed of 40 km/h. How fast must the train travel fo
next 150 km in order to maintain the average speed of 60 km/h for the entire journey?


please
give this answer quickly​

Answer 1

$\sf\small\underline\green{Given:-}$

$\sf{\implies Total\: distance=400km}$

$\sf\small\underline\green{To\: Find:-}$

$\sf{\implies speed\:of\: train=?}$

$\sf\small\underline\green{Given:-}$

we will solve this question by applying formula of time = Distance/speed.

$\sf\small\underline\green{Case-(i):-}$

$\sf{\implies Speed=40km/h\:\:\: Distance=250km}$

$\tt{\implies Time\:_{(1)}=\dfrac{Distance}{Speed}}$

$\tt{\implies Time\:_{(1)}=\dfrac{250}{40}}$

$\tt{\implies Time\:_{(1)}=\dfrac{25}{4}}$

$\sf{\implies Speed=x\:km/h\:\:\: Distance=150km}$

$\tt{\implies Time\:_{(2)}=\dfrac{Distance}{Speed}}$

$\tt{\implies Time\:_{(2)}=\dfrac{150}{x}}$

$\sf\small\underline\green{Case-(ii):-}$

$\tt{\implies Total\:_{(Distance)} = 400km}$

$\tt{\implies Total\:_{(Time)} =T\:_{(1)}+T\:_{(2)}}$

• Now speed of train in next case:-

$\tt{\implies Average\:_{(speed)}=\dfrac{Total\: distance}{Total\:time}}$

$\tt{\implies 60=\dfrac{400}{25/4+150/x}}$

$\tt{\implies 60=\dfrac{400}{(25x+600)/4x}}$

$\tt{\implies 60=\dfrac{1600x}{25x+600}}$

$\tt{\implies 60(25x+600)=1600x}$

$\tt{\implies 1500x + 36000=1600x}$

$\tt{\implies 1600x-1500x=36000}$

$\tt{\implies 100x=36000}$

$\tt{\implies x=360km/h}$

$\sf\large{Hence}$

$\bf{\implies Speed\:of\: train\:_{(next\:150km)}=360km/h}$

Answer 2

Given :-

On  a 400km track, a train travels the first 250 km at a uniform speed of 40 km/h.

To Find :-

How fast must the train travel next 150 km in order to maintain the average speed of 60 km/h for the entire journey?

Solution :-

We know that

Time = Distance/Speed

Let the speed be x

Now

Average Speed = Distance travelled/Time taken

60 = 400/(250/40) + (150/x)

60 = 400/(25/4 + 150/x)

60 = 400/(25 × x + 150 × 4/4x)

60 = 400/1 × 4x/25x + 600

60 = 400 × 4x/25x + 600

60 = 1600x/25x + 600

60 × (25x + 600) = 1600x

1500x + 36000 = 1600x

1600x - 1500x = 36000

100x = 36000

x = 36000/100

x = 360 km/h