Question

A car travels the first 30 km with a uniform speed of 60 km h⁻¹ and the next 30 km with a uniform speed of 40 km h⁻¹. Calculate :

1. The total time of journey,
2. The average speed of the car.

Answer 1

Given,

Distance travelled S₁ = 30 km

Speed v₁ = 60 km h⁻¹

Distance travelled S₂ = 30 km

Speed v₂ = 40 km h⁻¹

i. As we know,

`"Time" (t) = ("distance" (S))/("speed" (v))`

Substituting the values in the formula above, we get,

`t_1 = S_1/v_1`

= `30/60`

= `1/2` h

t₁ = 0.5 h

Converting 0.5 h to min we get,

⇒ t₁ = 0.5 × 60 min

⇒ t₁ = 30 min

and

`t_2 = S_2/v_2`

= `30/40`

= `3/4` h

t₂ ​= 0.75 h

Converting 0.75 h to min we get,

t₂ ​= 0.75 × 60 min

t₂ ​= 45 min

Total time t = t₁ + t₂

= 30 min + 45 min

= 75 min

Hence, Total time of journey = 75 min.

ii. As we know,

Total distance S = S₁ + S₂

= 30 km + 30 km

= 60 km

Hence, Total distance travelled = 60 km.

As we know,

`"Average speed" = "total distance"/"total time taken"`

= `60/1.25`

Average speed = 48 km h⁻¹

Hence, Average speed of the car = 48 km h⁻¹