Question

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

Answer 1

Answer:-

v = 90 km/hr

Given :-

For

s = 30 km, v = 30 km/hr

For next,

S = 90 km, v = ?

Average velocity = 60 km/hr

To find :-

The speed for next 90 km.

Solution:-

Let the speed for next 90 km be v km /hr.

Average speed → It is the ratio of the total distance covered by a body to total time take for whole journey.

Time taken for first journey,

t = s/v

t = 30 /30

t = 1 hr

Time taken for 2nd journey,

t = 90/v

From definition:-

$A_v = \dfrac{\text{Total distance travelled}}{\text{Total time taken}}$

Put the given value,

→$\mathsf{60 = \dfrac{30+90}{1 + \dfrac{90}{v}}}$

→$\mathsf{60 = \dfrac{120}{\dfrac{v + 90}{v}} }$

→$\mathsf{60 = \dfrac{120v}{v+90}}$

→$\mathsf{60 (v +90)= 120v }$

→$\mathsf{60v +5400 = 120v}$

→$\mathsf{5400 = 120v -60 v}$

→$\mathsf{5400 = 60v}$

→$\mathsf{v = \dfrac{5400}{60}}$

→$\mathsf{v = 90 km/hr}$

hence,

Speed for next 90 km is 90 km/hr.