Question

A car covers $\rm\bold{30km}$ at a uniform speed of $\rm\bold{30 m/hr}$. What should be its speed for the next $\rm\bold{90 km}$ if the average speed for the entire journey is $\rm\bold{60 km/h}$?

plz mod plz answer it​

Answer 1

Correct Question :-

A car covers 30km at a uniform speed of 30km/h . What should be it's speed for the next 90km if the average speed of the entire journey is 60km/h.

Given :-

• Distance covered by car ( in first) = 30km
• Speed of the car (in first ) = 30km/h
• Distance covered by car ( in next) = 90km
• Speed of the car ( in next) = ?
• Average speed of the car = 60km/h

To Find :-

• Speed of the car ( in next) = ?

Solution :-

To solve this at first we have find out total distance and total time taken by car then calculate the speed of can in the next case. Simply by applying formula of avarage speed = total distance / total time.

Calculation begin :-

• As we know that,

➞ Time = Distance/Speed

➞ T¹ = Distance¹/Speed ¹

• Here D = 30km. S = 30km/h

➞ T¹ = 30/30 = 1 hours

➞ T² = Distance²/Speed ²

• Here D = 90k. S = x km/h

➞ T² = 90/x hours

• Now total distance and time here:-

➞ Total time = T¹ + T²

➞ Total time = 1 + 90/x

➞ Total time = (x + 90)/x

➞ Total distance = 30 + 90 = 120km

• Now calculate speed of car in next :-

➞ Avarage speed = Total distance / total time

➞ 60 = 120 ÷ (x + 90)/x

➞ 60 = 120/1 × x/x + 90

➞ 60 = 120x / x + 90

➞ 120x = 60x + 5400

➞ 120x - 60x = 5400

➞ 60x = 5400

➞ x = 90km/h

Hence,

• Speed of the car in next = 90km/h

Answer 2

Answer:

Appropriate Question :-

• A car covers 30 km at a uniform speed of 30 km/h. What should be its speed for the next 90 km, if the average speed of the entire journey is 60 km/h.

Given :-

• A car covers 30 km at a uniform speed of 30 km/h. The speed for next is 90 km. The average speed of the entire journey is 60 km/h.

Solution :-

First, we have to find the time taken for the both cases :

${\normalsize{\bold{\purple{\underline{\bigstar\: In\: 1^{st}\: case\: :-}}}}}$

Given :

• Distance (d₁) = 30 km
• Speed (s₁) = 30 km/hr

As we know that,

$\mapsto \sf\boxed{\bold{\pink{Time =\: \dfrac{Total\: Distance}{Speed}}}}$

According to the question by using the formula we get,

$\implies \sf Time =\: \dfrac{d_1}{s_1}$

$\implies \sf Time =\: \dfrac{\cancel{30}}{\cancel{30}}$

$\implies \sf \bold{\green{Time =\: 1\: hrs}}$

${\normalsize{\bold{\purple{\underline{\bigstar\: In\: 2^{nd}\: case\: :-}}}}}$

Let,

$\mapsto$ Speed of car for next 90 km be y km/h

Given :

• Distance (d₂) = 90 km
• Speed (s₂) = y km/h

According to the question by using the formula we get,

$\implies \sf Time =\: \dfrac{d_2}{s_2}$

$\implies \sf Time =\: \dfrac{90}{y}$

$\implies \sf\bold{\green{Time =\: \dfrac{90}{y}\: hrs}}$

Now, we have to find the total distance covered and time taken :

${\normalsize{\bold{\purple{\underline{\bigstar\: In\: case\: of\: total\: distance\: covered\: :-}}}}}$

Given :

• Distance (d₁) = 30 km
• Distance (d₂) = 90 km

Then,

$\implies \sf Total\: distance\: covered =\: 30\: km + 90\: km$

$\implies \sf\bold{\green{Total\: distance\: covered =\: 120\: km}}$

${\normalsize{\bold{\purple{\underline{\bigstar\: In\: case\: of\: total\: time\: taken\: :-}}}}}$

Given :

• Time (t₁) = 1 hrs
• Time (t₂) = 90/y hrs

$\implies \sf Total\: time\: taken =\: 1\: hrs + \dfrac{90}{y}\: hrs$

$\implies \sf \bold{\green{Total\: time\: taken =\: \dfrac{y + 90}{y}\: hrs}}$

Now, we have to find the speed of car for next 90 km be y km/h :

As we know that,

$\clubsuit$ Average Speed Formula :

$\mapsto \sf\boxed{\bold{\pink{Average\: Speed =\: \dfrac{Total\: distance\: covered}{Total\: time\: taken}}}}$

Given :

• Average Speed = 60 km/h
• Total distance covered = 120 km
• Total time taken = y + 90/y

According to the question by using the formula we get,

$\longrightarrow \sf 60 =\: \dfrac{120}{\dfrac{y + 90}{y}}$

$\longrightarrow \sf 60 =\: \dfrac{120}{1} \times \dfrac{y}{y + 90}$

$\longrightarrow \sf 60 =\: \dfrac{120y}{y + 90}$

By doing cross multiplication we get,

$\longrightarrow \sf 120y =\: 60(y + 90)$

$\longrightarrow \sf 120y =\: 60y + 5400$

$\longrightarrow \sf 120y - 60y =\: 5400$

$\longrightarrow \sf 60y =\: 5400$

$\longrightarrow \sf y =\: \dfrac{540\cancel{0}}{6\cancel{0}}$

$\longrightarrow \sf y =\: \dfrac{\cancel{540}}{\cancel{6}}$

$\longrightarrow \sf y =\: \dfrac{90}{1}$

$\longrightarrow \sf\bold{\red{y =\: 90\: km/h}}$

$\therefore$ The speed of car for next 90 km is 90 km/h .