Question

A car travels at a speed of 50km/h for 30min , at 30km/h for the next 15min and then

at 70km/h for next 45min what is the average speed of car?
​

Answer 1

Answer:-

Given:-

Speed of the car in first 30 min = 50 km/h.

We know that,

Distance = Speed × time.

So,

⟹ Distance travelled by car in first 30 min = 50 × (30/60)

[ ∵ 1 minute = 1/60 hrs ]

⟹ Distance travelled by car in first 30 min = 25 km

Also given that,

Speed of the car for next 15 min = 30 km/hr

So, Distance travelled by the car for next 15 min = 30 × (15/60)

⟹ Distance travelled by the car for next 15 min = 7.5 km

Speed of the car in last 45 min = 70 km/h

⟹ Distance travelled by car in last 45 min = 70 × (45/60)

⟹ Distance travelled by car in last 45 min = 52.5 km

We know that,

Average speed = Total distance travelled/total time taken.

We have:-

• Total distance = (25 + 7.5 + 52.5) km = 85 km.

• Total time = 30 + 15 + 45 = 90 min = 90/60 hrs = 3/2 hrs.

So,

⟹ Average speed of the car = 85 / (3/2)

⟹ Average speed of the car = 85 × (2/3)

⟹ Average speed of the car = 56.66 km/hr

∴ The Average speed of the car is 56.66 km/hr.

Answer 2

Answer:

Given :-

• A car travels at a speed of 50 km/h for 30 minutes, 30 km/h for the next 15 minutes and then at 70 km/h for next 45 minutes.

To Find :-

• What is the average speed.

Formula Used :-

$\clubsuit$ Distance Formula :

$\longmapsto \sf\boxed{\bold{\pink{Distance =\: Speed \times Time}}}$

$\clubsuit$ Average Speed Formula :

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

Solution :-

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

$\mapsto$ A car travels at a speed of 50 km/h for 30 minutes :

Given :

• Speed = 50 km/h
• Time = 30 minutes = 30/60 = 0.5 hours

According to the question by using the formula we get,

$\implies \sf Distance =\: 50 \times 0.5$

$\implies \sf\bold{\green{Distance =\: 25\: km}}$

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

$\mapsto$ A car travels at a speed of 30 km/h for the next 15 minutes :

Given :

• Speed = 30 km/h
• Time = 15/60 = 0.25 hours

According to the question by using the formula we get,

$\implies \sf Distance =\: 30 \times 0.25$

$\implies \sf\bold{\green{Distance =\: 7.5\: km}}$

${\large{\bold{\purple{\underline{\bigstar\: In\: the\: {3}^{{rd}}\: case\: :-}}}}}$

$\mapsto$ A car travels at a speed of 70 km/h for next 45 minutes :

Given :

• Speed = 70 km/h
• Time = 45/60 = 0.75 hours

According to the question by using the formula we get,

$\implies \sf Distance =\: 70 \times 0.75$

$\implies\sf\bold{\green{Distance =\: 52.5\: km}}$

Now, we have to find the total distance travelled :

Given :

• d₁ = 25 km
• d₂ = 7.5 km
• d₃ = 52.5 km

$\leadsto \sf Total\: distance\: travelled =\: 25 + 7.5 + 52.5$

$\leadsto \sf\bold{\green{Total\: distance\: travelled =\: 85\: km}}$

Again, we have to find the total time taken :

Given :

• t₁ = 0.5 minutes
• t₂ = 0.25 minutes
• t₃ = 0.75 minutes

$\leadsto \sf Total\: time\: taken =\: 0.5 + 0.25 + 0.75$

$\leadsto \sf\bold{\green{Total\: time\: taken =\: 1.5\: hours}}$

Now, we have to find the average speed :

Given :

• Total distance travelled = 85 km
• Total time taken = 1.5 hours

According to the question by using the formula we get,

$\dashrightarrow \sf Average\: Speed =\: \dfrac{85}{1.5}$

$\dashrightarrow \sf Average\: Speed =\: \dfrac{85}{\dfrac{15}{10}}$

$\dashrightarrow \sf Average\: Speed =\: \dfrac{85}{1} \times \dfrac{10}{15}$

$\dashrightarrow \sf Average\: Speed =\: \dfrac{850}{15}$

$\dashrightarrow\sf\bold{\red{Average\: Speed =\: 56.66\: km/h}}$

$\therefore$ The average speed of car is 56.66 km/h.