Question

A car covers 30km at a uniform speed of 30km/hr. what should be its speed
for the next 90km if the average speed for the entire journey is 60km/h?​

Answer 1

A car covers 30km at a uniform speed of 30km/hr.

Here; distance is 30 km and speed is 30 km/hr.

Now,

Time = Distance/Speed

t1 = 30/30 = 1 hr

The distance covered by the car in second half is 90 km.

Let us assume that the car is moving with a speed of x km/hr.

t2 = 90/x hr

Also, given that the average speed of the car is 60 km/hr.

Average speed is defined as the ratio of total distance covered with respect to total time taken.

Total distance covered by the car = (30 + 90) km = 120 km

Total time taken by car = t1 + t2

= (1 + 90/x) hr

Average speed = (Total distance covered)/(Total time taken)

60 = 120/(1 + 90/x)

1 = 2/(1 + 90/x)

1/2 = 1/[(90 + x)/x]

1/2 = x/(90 + x)

90 + x = 2x

90 = x

Therefore, the speed of the car in second half is 90 km/hr.

Answer 2

${ \bold{ \huge{ \underline{ \red{ \underline{Question:-}}}}}}$




▪ A car covers 30 km at a uniform speed of 30 km/hr . what should be it's speed for the next 90 km, if the average speed for the entire journey is 60 km/hr ?




${ \bold{ \huge{ \underline{ \red{ \underline{Solution:-}}}}}}$



${ \bold{ \purple{GIVEN-}}}$



➡ A car covers 30 km at a uniform speed of 30 km/hr



❃ Distance 1 ( D1 ) = 30 km



❃ Speed 1 ( S1 ) = 30 km/hr



❃ Time taken ( T1 ) = distance 1/ speed



= 30 km / (30km/hr)



= 1 hr



${ \bold{ \purple{TO \: FIND- }}}$



▪ The speed for next 90 km of the average speed is 60 km/hr ????



⫸ Let the speed for next 90 km be x km/hr..




Then,


❃ Distance 2 ( D2 ) = 90 km



❃ Speed 2 ( S2 ) = x km/hr



❃ Time 2 ( T2 ) = 90km / ( x km/hr)



= 90/x hr



${ \dagger{ \bold{ \pink{ \underline{ \: \: \: average \: speed}}}}}$



The average speed of an object is the total distance traveled by the object divided by the elapsed time to cover that distance. It's a scalar quantity which means it is defined only by magnitude. ...



${ \boxed{ \bold{ \red{average \: speed = \frac{total \: distance \: covered}{total \: time \: taken}}}}}$



➡ it's given in the question that the average speed of the car is 60 km/hr




${ \bold{average \: speed = \frac{d1 \: + \: d2}{t1 \: + \: t2}}}$




${ \bold{60km {hr}^{ - 1} = \frac{30km \: + \: 90km}{1hr \: + \: \frac{90}{x}hr}} }$




${ \bold{ \implies{60km {hr}^{ - 1} = \frac{120 \: km}{ \frac{(x + 90)}{x}hr}}} }$




${ \bold{ \implies{ \frac{x + 90}{x} = 2}}}$




${ \bold{ \implies{x + 90 = 2x}}}$




${ \bold{ \implies{2x - x = 90}}}$




${ \boxed{ \boxed{ \bold{ \implies{ \pink{x = 90 \: km \: {hr}^{ - 1}}}}}}}$




therefore,



➡ the speed of the car for next 90 km must be 90 km/ hr , if the average speed for the entire journey is 60 km/hr