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Dolly drives her car on a straight highway at a uniform rate of $40 km$ $h^{- 1}$ for $2 hours$ and then at a uniform rate of $70 km$ $h^{- 1}$ for $1 hour$ . Calculate her average speed for the entire journey.

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30.9 km h^{- 1}

50 km h^{- 1}

30 km h^{- 1}

10 km h^{- 1}

answer is B.

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Detailed Solution

Given data in the problem,
Uniform speed of car,

v_{1} = 40 km h^{- 1}

Time taken,

t_{1} = 2 h

Uniform speed of car,

v_{2} = 70 km h^{- 1}

Time taken,

t_{2} = 1 h

So,
Distance

s_{1}

travelled by dolly in time

t_{1}

is given by

{= > s}_{1} = v_{1} \times t_{1}

{= > s}_{1} = 40 \times 2

{= > s}_{1} = 80 km

Distance

s_{2}

travelled by dolly in time

t_{2}

is given by

= > s_{2} = v_{2} \times t_{2}

{= > s}_{2} = 70 \times 1

= > s_{2} = 70

By using the speed formula,
Average speed,

v_{av} = \frac{Total distance travelled}{Total time taken}

= > v_{av} = \frac{s_{1} + s_{2}}{t_{1} + t_{2}}

= > v_{av} = \frac{80 + 70}{2 + 1}

= > v_{av} = \frac{150}{3}

= > v_{av} = 50 km h^{- 1}

So, the average speed for the entire journey is

50 km h^{- 1}

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