Average_Speed

Algebra Level 2

A car travels first half of the distance between two places at a speed of 40 40 km/hr and the second half at 60 60 km/hr. What is the average speed of the car in km/hr?


The answer is 48.

Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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1 solution

Naren Bhandari
Jul 25, 2018

Average Speed = total distance travelled total time taken \text{Average Speed} = \dfrac{\text{total distance travelled }}{\text{total time taken}} Let L 1 , L 2 , T 1 L_1 , L_2 , T_1 and T 2 T_2 are distance travelled and time taken in first and second half. ∴ V A = L 1 + L 2 T 1 + T 2 = L 1 + L 2 L 1 V 1 + L 2 L 2 V A = 2 V 1 V 2 V 1 + V 2 = 2 ⋅ 48 ⋅ 50 60 + 40 = 48 \therefore V_{A} = \dfrac{L_1+L_2}{T_1+T_2} = \dfrac{L_1+L_2 }{\frac{L_1}{V_1} + \frac{L_2}{L_2}} \\ V_A = \dfrac{2V_1 V_2}{V_1+V_2} =\dfrac{2\cdot 48\cdot 50}{60+40} =\boxed{48}

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