A car travels with speed $30 k m h^{- 1}$ for $30$ minute and then with speed $40 k m h^{- 1}$ for one hour. Find :
(a)the total distance travelled by the car
(b)the total time of travel, and
(c)the average speed of car.

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Solution

Given, Time travelled $(t_{1}) = 0.5 h$
Speed during $0.5 h, (s_{1}) = 30 k m h^{- 1}$
Time travelled $(t_{2}) = 1.0 h$
Speed during $1 h, (s_{2}) = 30 k m h^{- 1}$
To find, Total distance travelled $(d_{1})$
Total time taken (t)
Average speed

(a) $Total distance travelled (d)$
$= Distance travelled in 30 m i n . (d_{1}) + Distance travelled in next 1 h o u r (d_{2})$
$d = (s_{1} \times t_{1}) + (s_{2} \times t_{2})$
$d = (30 k m h^{- 1} \times 0.5 h) + (40 k m h^{- 1} \times 1 h)$
$d = 15 k m + 40 k m$
$d = 55 k m$

(b)Total time $(t) = t_{1} + t_{2}$
$= 0.5 h + 1.0 h$

The total time of journey is $1.5 h$ .

(c) $Average speed = \frac{Total distance covered}{Total time taken}$
$= \frac{55 k m}{1.5 h r}$
The average speed during journey is $36.67 k m h^{- 1}$ .

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