Question

A car travels on a straight country highway for 5 km at 100 km/hr. then through a populated area for another 5 km at 60 km/hr .the average velocity of the car is
A)80 km/hr
B)75 km/hr
C)310 km/hr
D)64 km/hr​

Answer 1

Ans :- B) 75 km/hr.................

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$1. \: \: \: \displaystyle \sf{Average \: Velocity = \: \frac{Total \: Distance \: covered }{Total \: time \: taken} \: \: \: }$

2. Time taken to travel a distance

$\displaystyle \sf{= \: \frac{Total \: Distance \: covered }{ \: Velocity } \: \: \: }$

GIVEN

A car travels on a straight country highway for 5 km at 100 km/hr. then through a populated area for another 5 km at 60 km/hr

TO DETERMINE

The average velocity of the car

CALCULATION

A car travels on a straight country highway for 5 km at 100 km/hr

So in this duration velocity was

$= \displaystyle \: \sf{ \: 100 \: \: km/hr\: }$

$= \displaystyle \: \sf{ \: \frac{100}{60} \: \: km/min\: }$

Time taken to travel 5 km

$= \displaystyle \: \sf{ \: 5 \times \frac{60}{100} \: \: min\: }$

$= \displaystyle \: \sf{ \: 3 \: \: min }$

Again The car travels through a populated area for another 5 km at 60 km/hr

So in this duration velocity was

$= \displaystyle \: \sf{ \: 60 \: \: km/hr\: }$

$= \displaystyle \: \sf{ \: \frac{60}{60} \: \: km/min\: }$

$= \displaystyle \: \sf{ \: 1 \: \: km/min\: }$

Time taken to travel 5 km

$= \sf{ \: 5 \times 1 \: \: \: min \: }$

$= \sf{ \: 5 \: \: \: min \: }$

So total distance covered

$= \sf{ \: (5 + 5) \: \: \: km \: \: }$

$\sf{ \: = 10 \: \: km\: }$

Total time taken

$\sf{ \: =( \: 5 + 3 \: ) \: \: min \: }$

$\sf{ \: =8 \: \: min \: }$

Hence

$\displaystyle \sf{Average \: Velocity }$

$\displaystyle \sf{ = \: \frac{Total \: Distance \: covered }{Total \: time \: taken} \: \: \: }$

$\displaystyle \sf{ = \frac{10}{8} \: \: km/min \: \: }$

$\displaystyle \sf{ = \frac{10 \times 60}{8} \: \: \: \: km/hr \: \: }$

$\displaystyle \sf{ = 75 \: \: \: \: km/hr \: \: }$