Question

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A car travels first 30 km with a
uniform speed of 60 km h-1 and the
30 km with a uniform speed
of 40 km h-1 Calculate :
1) the total time of journey
2) the average speed of car​

Answer 1

Answer :-

• Total time taken = 1 hour 15 minutes or 75 minutes.

• Average speed = 48 Km/h

Given :-

• A car travels first 30 km with a uniform speed of 60 km/h and the 30 km with a uniform speed of 40 km/h.

To Find :-

• The total time taken in completing the journey.

• The average speed of the car.

Step By Step Explanation :-

As given A car travels first 30 km with a uniform speed of 60 km/h and the 30 km with a uniform speed of 40 km/h.

We need to find the total time taken to complete the journey.

Let the time for the first journey be x and time for second journey be y.

$\dag \boxed{ \bf{ \purple{Speed = \cfrac{Distance}{Time}}}}$

By substituting the values ⤵

For first journey ⤵

$\implies \tt60 = \cfrac{30}{x} \\ \\ \implies \tt60x = 30 \\ \\ \implies \tt \: x = \cancel \cfrac{30}{60} \\ \\\implies \tt x = \cfrac{1}{2} \: of \: a \: hour. \\ \\ \implies \tt\cfrac{1}{ \not2} \times \not6 \not0 \\ \\ \implies \tt30 \: minutes$

For second journey ⤵

$\implies \tt40 = \cfrac{30}{y} \\ \\ \implies \tt 40y = 30 \\ \\ \implies \tt y = \cancel \cfrac{30}{40} \\ \\ \implies \tt y = \cfrac{3}{4} \: of \: a \: hour. \\ \\ \implies \tt \cfrac{3}{ \not4} \times \not6 \not0 \\ \\ \implies \tt45 \: minutes$

Total time taken = 30 + 45 minutes => 75 minutes or 1 hour 15 minutes.

Now we need to calculate average speed.

$\dag\boxed{\red{\bf{Average\:Speed=\cfrac{Total\:Distance}{Total\:Time\:Taken}}}}$

We can also write time as 75/60 hours

By substituting the values ⤵

$\implies \tt \: Average \: Speed = \cfrac{30 + 30}{ \cfrac{75}{60} } \\ \\ \implies\tt\cancel\cfrac{60\times 60}{75} \\ \\ \implies\bf Average \: Speed = 48 Km/h$

Therefore average speed = 48 Km/h

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