Question

A car travels 30 km at a uniform speed of 40 km/h and
the next 30 km at a uniform speed of 20 km/h. Find its
average speed
​

Answer 1

Given

A car travels 30 km at a uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h.

To find

Find its average speed

Solution

★ A car travels 30 km at a uniform speed of 40 km/h

• Distance travelled = 30km
• Speed = 40km/h
• Time taken = ?

**Let the time be t1**

→ Time = distance/speed

→ t1 = 30/40 = 3/4h

★ The car travels next 30 km at a uniform speed of 20 km/h.

• Distance travelled = 30km
• Speed = 20km/h
• Time taken = ?

**Let the time be t2**

→ Time = distance/speed

→ t2 = 30/20 = 3/2h

Now, Average speed

→ total distance travelled/total time taken

= 30 + 30/t1 + t2

= 60/3/4 + 3/2

= 60/3 + 6/4

= 60/9/4

= 60 × 4/9 = 26.6 km/h

Hence, the average speed of car is 26.6km/h

Answer 2

Given:-

Case 1:-

• Speed = 40 km/h (Uniform), [v]
• Distance travelled = 30 km [s]

Case 2:-

• Speed = 20 km/h [v′]
• Distance travelled = 30 km [s′]

To Find: Average speed of the whole trip.

We know,

Average speed = (Total distance travelled)/(Total time taken)

Total distance travelled = s + s′

= 30 km + 30 km

= 60 km

Finding total time taken:-

We know,

t = s/v

Case 1:-

t = (30 km)/(40 km/h)

→ t = ¾ h

Case 2:-

t′ = (30 km)/(20 km/h)

→ t′ = 3/2 h

∴ Average speed = (60 km)/(t + t′)

= (60 km)/(¾ h + 3/2 h)

= (60 km)/(9/4 h)

= (60 × 4 km)(9 h)

= (80 km)(3 h)

≈ 26.66 km/h

∴ AVERAGE SPEED OF THE WHOLE TRIP WAS APPROXIMATELY (26.66 KM/H).