Question

A car moves with a speed of 30 km · h-1 in half of the
total time taken and with 40 km.h-1 rest of the time.
What is the average speed of the body? [35 km.h -1]​

Answer 1

${\underline{\sf{Question}}}$

A car moves with a speed of 30 km/ht in half of the total time taken and with 40 km/hr rest of the time.What is the average speed of the body?

${\underline{\sf{Solution}}}$

Let the total time taken by the car be ' t ' hour .

According to the question :

A car moves with a speed of 30 km/ht in half of the total time taken .

⇒ Speed = 30km /hr

time = t /2

Therefore ,Distance covered

$\sf\:D_{1} =speed\times\:time$

$\sf\:D_{1}=30\times\frac{t}{2}$

$\sf\:D_{1}=15t$

and A car moves with 40 km/hr for rest of the time.

⇒Speed = 40 km/hr and time = t/2

Thus ,Distance covered

$\sf\:D_{2} =speed\times\:time$

$\sf\:D_{2} =40\times\dfrac{t}{2}$

$\sf\:D_{2}=20t$

We know that

Average speed

= total distance / total time

$\sf\ =\dfrac{D_{1}+D_{2}}{t}$

$\sf\ =\dfrac{20t+15t}{t}$

$\sf\ =\dfrac{35t}{t}$

= 35km/hr

Therefore the average speed of the car=35km/hr.

$\rule{200}2$

More About the topic :

• speed is the distance travelled in unit time .

Speed = distance / time

Thus , distance = speed × time

• Average speed = total distance / total time

Answer 2

GiveN :-

♠ Time taken by the car to travel a certain distance is x hours.

♠ It travels with speed 30 km/h in half of the time taken (i.e. x/2 hours).

♠ Again, it travels with speed 40 km/h in the other half time (i.e. x/2 hours).

TO DeterminE :-

The average speed of the body.

AcknowledgemenT :-

♠ Distance = Speed × Time

♠ Average speed = Total distance covered/Total time taken

SolutioN :-

CASE-I

Speed = 30 km/h

Time = x/2 hours

Distance = 30 × x/2

⇒Distance = 15x km

$\rule{120}{2}$

CASE-II

Speed = 40 km/h

Time = x/2 hours

Distance = 40 × x/2

⇒Distance = 20x km

$\rule{120}{2}$

Total distance covered = 15x + 20x = 35x km

Total time taken = x hours

☛ Average speed = Total distance covered/Total time taken

⇒Average speed = 35x/x

⇒Average speed = 35 km/h

Therefore, the average speed of the body is 35 km/h or 35 km.h⁻¹.