Question

A car travelling at a uniform speed covers a distance of $165$ Km in $3$ hours . At that same speed , (a) How long will it take to cover a distance of $330$ Km ? (b) How far will it travel in $8$ hours ?

Answer 1

Hint: As in the question first find out the speed of the car by formula ${\text{Speed = }}\dfrac{{{\text{Distance }}}}{{{\text{Time}}}}$ where Distance = $165$ Km and the Time taken = $3$ hours hence it is given that the speed is constant . In (a) part use ${\text{Time = }}\dfrac{{{\text{Distance }}}}{{{\text{Speed}}}}$ where distance = $330$ Km and in (b) part use ${\text{Distance = Speed }} \times {\text{ Time }}$where Time = $8$ hours .

Complete step-by-step answer:
In this question it is given that the car travelling at a uniform speed covers a distance of $165$ Km in $3$ hours , So the speed of the car will be
${\text{Speed = }}\dfrac{{{\text{Distance }}}}{{{\text{Time}}}}$
So from given the Distance = $165$ Km and the Time taken = $3$ hours
Therefore ,
$\Rightarrow$ Speed = $\dfrac{{165}}{3}$ = $55$ Km/hr
So in the question it is given that the speed is constant
(a) In this it will asked that how much time it will take to cover $330$ Km
As we know that the ${\text{Speed = }}\dfrac{{{\text{Distance }}}}{{{\text{Time}}}}$ ,
Hence ${\text{Time = }}\dfrac{{{\text{Distance }}}}{{{\text{Speed}}}}$
So distance = $330$ Km and Speed = $55$ Km/hr given in the question
Therefore Time = $\dfrac{{330}}{{55}}$ = $6$ hours
(b) In this it will asked that if the car will travel with same speed then how much it will travel in $8$ hours
So we know that the
${\text{Distance = Speed }} \times {\text{ Time }}$
So Speed = $55$ Km/hr and Time = $8$ hours
$\Rightarrow$ ${\text{Distance = 55 }} \times {\text{ 8}}$ = $440$
Hence $440$ km it will travel in $8$ hours .

Note: In the (a) part we also solve with unitary method as it is given the car travelling at a uniform speed covers a distance of $165$ Km in $3$ hours so we have to find how much time it will take to complete $330$ km so it is twice of $165$ hence time will twice that is $6$ hours .
Sometimes in the question average speed is given to find the formula of average speed is equal to
Average speed = $\dfrac{{Total{\text{ }}distance{\text{ }}travel}}{{Total{\text{ }}time{\text{ }}taken}}$