Question

A car travels first 30 km with a uniform speed of
60 km h-1and then next 30 km with a uniform speed
of 40 km h-1 Calculate : (i) the total time of journey,
(ii) the average speed of the car,
Ans.(i) 75 min, (ii) 48 km h-1​

Answer 1

Answer:

Total time = 75 minutes

Average speed = 48 km/h

Explanation:

As per the provided information in the given question, we have :

• Speed of car to cover first 30 km = 60 km/h
• Speed of car to cover next 30 km = 40 km

We are asked to calculate the total time of journey and the average speed.

Calculating total time taken :

Total time taken will be equivalent to sum of time taken to cover first 30 km and time taken to cover next 30 km.

$\longmapsto \rm {Time_{(Total)} = Time_{(1st \; 30 \; km)} + Time_{(2nd \; 30 \; km)} }$

$\longmapsto \rm {Time_{(Total)} = \dfrac{Distance_{(1st \; 30 \; km)}}{Speed_{(1st \; 30 \; km)}} + \dfrac{Distance_{(2nd \; 30 \; km)}}{Speed_{(2nd \; 30 \; km)}} }$

$\longmapsto \rm {Time_{(Total)} = \Bigg ( \dfrac{30}{60} + \dfrac{30}{40} \Bigg ) \; hr }$

$\longmapsto \rm {Time_{(Total)} = \Bigg ( \dfrac{60+90}{120} \Bigg ) \; hr }$

$\longmapsto \rm {Time_{(Total)} = \Bigg ( \dfrac{150}{120} \Bigg ) \; hr }$

$\longmapsto \rm {Time_{(Total)} = \dfrac{15}{12} \; hr }$

Now, converting hours to minutes :

• 1 hour = 60 minutes

$\longmapsto \rm {Time_{(Total)} = \Bigg ( \dfrac{15}{12} \times 60 \Bigg ) \; minutes }$

$\longmapsto \rm {Time_{(Total)} = \Big ( 15 \times 5 \Big ) \; minutes }$

$\longmapsto \bf {Time_{(Total)} = 75 \; minutes }$

∴ Total time taken to cover whole journey is 75 minutes.

$\rule{200}2$

Calculating average speed :

$\longmapsto \bf {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }$

$\longmapsto \rm {Speed_{(avg)} = \dfrac{(30+30) \; km}{\cfrac{15}{12} \; h} }$

$\longmapsto \rm {Speed_{(avg)} = \dfrac{60 \; km}{\cfrac{15}{12} \; h} }$

$\longmapsto \rm {Speed_{(avg)} =\Bigg ( 60 \times \dfrac{12}{15}\Bigg ) \; kmh^{-1} }$

$\longmapsto \rm {Speed_{(avg)} =\Big ( 4 \times 12 \Big ) \; kmh^{-1}}$

$\longmapsto \bf {Speed_{(avg)} = 48 \; kmh^{-1} }$

∴ Average speed of the car is 48 km/h.

$\rule{200}2$