Question

Ch-8 Linear equations in one variable
11)The speed of an express train is 10 km/h slower than the speed of a superfast train. If the superfast train takes 30 minutes to cover a distance of 80 km, find the time taken by the express train to cover. this distance. ​

Answer 1

☆Given :

$\rightarrow$ distance covered by superfast train = 80km

$\: \: \: \:$$\rightarrow$ Time = 30 min

$\huge \bigstar \mathfrak{ \: solution :}$

$\rightarrow$ Speed of superfast train in hrs

$= \huge\frac{80 \times 60}{30}$

= 80 × 2

= 160 km/hr

$\: \: \: \:$$\therefore$ Speed of train :

= 160 - 10

$\: \: \: \:$= 150 km/hr

$\rightarrow$ speed of train in 30 min :

$\: \: \: \:$$= \: \huge\frac{150}{2}$

= $\large \red{75 km}$

$\therefore$ distance = 75 km

$\: \: \: \:$$\bigstar$ Time = 75 ÷ 2

$\large \boxed{time \: = \: 32.5 min}$

Answer 2

Given that, The speed of an express train is 10 less than the speed of a superfast train.

Also, The superfast train takes 30 minutes to cover a distance of 80km.

Let the speed of express train and superfast train be x and y respectively.

According to the question,

⇒ Express train's speed + 10 = Superfast train's speed

⇒ x + 10 = y

⇒ x - y = -10 ...(1)

Again,

⇒ Time taken by superfast train to cover a distance of 80km = 30 minutes

Convert time into hour.

∵ 1 hour = 60 minutes

∴ 30 minutes = 0.5 hour

⇒ Distance = Speed × Time

⇒ 80 = y × 0.5

⇒ y = 80 / 0.5

⇒ y = 160

Substitute [y = 160] in (1)

⇒ x - 160 = -10

⇒ x = 160 - 10

⇒ x = 150

Now,

⇒ Time taken by express train to cover a distance of 80km = Distance / Speed

⇒ Time taken = 80 / 150

⇒ Time taken = 0.53 hour

or, Time taken = 31.8 minutes

Or, Time taken ≈ 32 minutes.

Hence, Time taken by the express train to cover a distance of 80 km is approx. 32 minutes.