Question

Two cities p and q are 360 km apart. a vehicle goes from p to q with a speed of 40 km/hr and returns to p with a speed of 60 km/hr. what is the average speed of the vehicle?

a.55

b.52

c.50

d.48

Answer 1

Answer:

Option D (48 km/h)

Explanation:

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

• Two cities P and Q are 360 km apart.
• A vehicle goes from P to Q with a speed of 40 km/hr and returns to P with a speed of 60 km/hr.

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

As we know that,

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

So, in order to calculate the average speed, we need to find the total distance travelled and total time taken first.

$\underline{ \pmb { \sf { Total \; distance :}}}$

Since, the body goes from P to Q and returns from Q to P. So,

$\longmapsto \rm {Distance_{(Total)} = Distance_{(PQ)} + Distance_{(QP)} }$

$\longmapsto \rm {Distance_{(Total)} = (360 + 360) \; km }$

$\longmapsto \bf {Distance_{(Total)} = 720 \; km }$

∴ Total distance covered is 720 km.

$\underline{ \pmb { \sf { Total \; time :}}}$

$\longmapsto \rm {Time_{(Total)} = Time_{(PQ)} + Time_{(QP)} }$

• Time = Distance/Speed

$\longmapsto \rm {Time_{(Total)} = \dfrac{Distance_{(PQ)} }{Speed_{(PQ)} } + \dfrac{Distance_{(QP)} }{Speed_{(QP)} } }$

$\longmapsto \rm {Time_{(Total)} = \Bigg ( \dfrac{360 }{40} + \dfrac{360 }{60} \Bigg )\; h}$

$\longmapsto \rm {Time_{(Total)} = \Bigg ( 9 + 6 \Bigg )\; h}$

$\longmapsto \bf {Time_{(Total)} = 15 \; h}$

∴ Total time taken is 15 hours.

$\underline{ \pmb { \sf { Average \; speed :}}}$

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

$\longmapsto \rm {Speed_{(avg)} = \dfrac{720 \; km}{15 \; h} }$

$\longmapsto \bf {Speed_{(avg)} = 48 \; kmh^{-1} }$

∴ Average speed of the vehicle is 48 km/h.