Question

10. A car moves with a speed of 30 km/h-1 for hal
an hour, 25 km/h-1 for one hour and 40 km/h-1 for
two hours. Calculate the average speed of the car​

Answer 1

Answer:

34.285 km/h

Explanation:

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

• A car moves with a speed of 30 km/h for half an hour.
• Then, 25 km/h for one hour.
• After that, 40 km/h for 2 hours.

We are asked to calculate the average speed of the car.

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

Calculating total distance :

$\longmapsto \rm {S_{(Total)} = S_1 + S_2 + S_3 }$

• S denotes distance
• Distance = Speed × Time

$\longmapsto \rm {S_{(Total)} = (V_1 T_1) + (V_2 T_2) + (V_3T_3) }$

$\longmapsto \rm {S_{(Total)} = \Bigg ( 30 \times \dfrac{1}{2} \Bigg ) \; km + \Bigg ( 25 \times 1 ) \; km + \Bigg ( 40 \times 2 \Bigg ) \; km }$

$\longmapsto \rm {S_{(Total)} = 15 \; km + 25 \; km + 80 \; km }$

$\longmapsto \boxed{\bf {S_{(Total)} = 120 \; km }}$

Calculating total time :

$\longmapsto \rm {T_{(Total)} = T_1 + T_2 + T_3 }$

$\longmapsto \rm {T_{(Total)} = \Bigg ( \dfrac{1}{2} + 1 + 2 \Bigg ) \; h }$

$\longmapsto \rm {T_{(Total)} = \Bigg ( \dfrac{1}{2} + 3 \Bigg ) \; h }$

$\longmapsto \rm {T_{(Total)} = \Bigg ( \dfrac{1 + 6 }{2} \Bigg ) \; h }$

$\longmapsto \boxed{ \bf {T_{(Total)} =\dfrac{7 }{2} \; h }}$

Calculating average speed :

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

$\longmapsto \rm {Speed_{(avg)} = \Bigg ( 120 \div \dfrac{7}{2} \Bigg ) \; kmh^{-1} }$

$\longmapsto \rm {Speed_{(avg)} = \Bigg ( 120 \times \dfrac{2}{7} \Bigg ) \; kmh^{-1} }$

$\longmapsto \rm {Speed_{(avg)} = \Bigg ( \dfrac{240}{7} \Bigg ) \; kmh^{-1} }$

$\longmapsto \boxed {\bf {Speed_{(avg)} = 34.285 \; kmh^{-1} }}$

∴ Average speed of the car is 34.285 km/h.

Answer 2

Q]__?

Solution:

Distance = speed × time

Average Speed = Total distance/ Total time

[ To Find Avg speed first we have to find total distance and total time ]

The distance Covered when he moves with the speed of 30 km/h for half and hour,

Distance = 30 × 1/2 = 15 km _[i]

The distance Covered when he moves with the speed of 25 km/h for one hour,

Distance = 25 × 1 = 25 km _[ii]

Now, The distance Covered when he moves with the speed of 40 km/h for two hour,

Distance = 40 × 2 = 80 km _[iii]

...[ Adding Equation [i], [ii] and [iii] ]

Total Distance = 15 + 25 + 80

= 120 km

Total time Time taken = 0.5 + 1+ 2

= 3.5 hr

Hence Average speed = 120/ 3.5

= 34. 286 km/hr

∴The average speed of the car is 34.286 km/h

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