Question

5. A car travels at a speed of 40 km h for 0.50 h, at 20 km h for next 0.3 h and then at 70 km h for next 0.67 h. What is the average speed of the car?​

Answer 1

Answer :

• Average speed of car = 49.6 km h¯¹

Step-by-step explanation :

In this case, we need to calculate the distance travelled by the car under three different conditions of speed and time.

(i). In the first case, the car travels at a speed of 40 km h¯¹ for a time of 0.50 hours.

Speed = Distance travelled/ Time taken

Distance = Speed x Time

= 40 x 0.50 = 20 km

.......... (1)

(ii). In the second case, the car travels at a speed of 20 km h¯¹ for a time of 0.3 hours.

Speed = Distance travelled/Time taken

Distance = Speed x Time

= 20 x 0.30 = 6 km ......(2)

(iii). In the third case, the car travels at a speed of 70 km h¯¹ for a time of 0.67 hours.

Speed = Distance travelled/ Time taken

Distance = Speed x Time

= 70 x 0.67 = 46.9 km ...... (3)

From the equations (1), (2) and (3), we get

Total distance travelled

= 20 + 6 + 46.9% = 72.9 km

Total time taken = 0.50 + 0.30 + 0.67 = 1.47 h

Average speed = Total distance travelled/Total time taken

= 72.9/1.47 = 49.6 km h¯¹

Answer 2

$\large \blue{\bf 1st \: case}$

• Speed = 40 km/h
• Time = 0.50 h
• Distance = ?

$\boxed{ \bf Distance = Speed \times Time} \\ \\ \bf \Longrightarrow40 \times 0.50 \\ \\ \bf \Longrightarrow20km$

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$\large</strong><strong>\</strong><strong>b</strong><strong>l</strong><strong>u</strong><strong>e</strong><strong>{</strong><strong> \bf 2nd \: case</strong><strong>}</strong><strong>$

• Speed = 20 km/h
• Time = 0.3 h
• Distance = ?

$\bf Distance = Speed \times Time \\ \\ </strong><strong> </strong><strong> \bf</strong><strong> </strong><strong>\</strong><strong>L</strong><strong>o</strong><strong>n</strong><strong>g</strong><strong>r</strong><strong>i</strong><strong>g</strong><strong>h</strong><strong>t</strong><strong>a</strong><strong>r</strong><strong>r</strong><strong>o</strong><strong>w</strong><strong>20 \times 0.3 \\ \\ \bf</strong><strong> </strong><strong>\</strong><strong>L</strong><strong>o</strong><strong>n</strong><strong>g</strong><strong>r</strong><strong>i</strong><strong>g</strong><strong>h</strong><strong>t</strong><strong>a</strong><strong>r</strong><strong>r</strong><strong>o</strong><strong>w</strong><strong>6 \: km$

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$\large</strong><strong> </strong><strong>\</strong><strong>b</strong><strong>l</strong><strong>u</strong><strong>e</strong><strong>{</strong><strong> \bf 3rd \: case</strong><strong>}</strong><strong>$

• Speed = 70 km/h
• Time = 0.67 h
• Distance = ?

$\bf Distance = Speed \times Time \\ \\ \bf</strong><strong> </strong><strong>\</strong><strong>L</strong><strong>o</strong><strong>n</strong><strong>g</strong><strong>r</strong><strong>i</strong><strong>g</strong><strong>h</strong><strong>t</strong><strong>a</strong><strong>r</strong><strong>r</strong><strong>o</strong><strong>w</strong><strong> 70 \times 0.67 \\ \\ \bf</strong><strong> </strong><strong>\</strong><strong>L</strong><strong>o</strong><strong>n</strong><strong>g</strong><strong>r</strong><strong>i</strong><strong>g</strong><strong>h</strong><strong>t</strong><strong>a</strong><strong>r</strong><strong>r</strong><strong>o</strong><strong>w</strong><strong>46.9 \: km$

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$\bf Total \: distance = 20 + 6 + 46.9 \\ \\ \bf </strong><strong>\</strong><strong>L</strong><strong>o</strong><strong>n</strong><strong>g</strong><strong>r</strong><strong>i</strong><strong>g</strong><strong>h</strong><strong>t</strong><strong>a</strong><strong>r</strong><strong>r</strong><strong>o</strong><strong>w</strong><strong>72.9km$

$\bf Total \: time = 0.50 + 0.3 + 0.67 \\ \\ \bf</strong><strong> </strong><strong>\</strong><strong>L</strong><strong>o</strong><strong>n</strong><strong>g</strong><strong>r</strong><strong>i</strong><strong>g</strong><strong>h</strong><strong>t</strong><strong>a</strong><strong>r</strong><strong>r</strong><strong>o</strong><strong>w</strong><strong>1.47 \: h \:$

$\bf Average \: speed = \frac{ distance}{ time} \\ \\ \bf Average \: speed = \frac{72.9}{1.47} \\ \\ \underline{ \boxed{ \green{ \bf Average \: speed = 49.</strong><strong>6</strong><strong> km/h }}}$