Question

Total journey of a bus is 600km. IT travels 120 km at the speed of 40km/h.what should be the speed for next 480km so that average speed is 60km/h.
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Answer 1

Given:

Total distance covered by bus= 600 Km

Distance travelled by bus with speed of 40 km/h = 120 Km

Average speed of bus for journey= 60 Km/h

To Find:

Speed of bus when it travelled remaining 480 Km

Solution:

Let the time taken by bus for covering first 120 Km be t₁, time taken by bus for covering next 480 Km be t₂ and speed of bus for last 480 Km be 'v' Km/h

We know that,

$\pink{\boxed{\rm{Average\:Speed=\dfrac{Total\:distance\:covered}{Total\:time\:taken}}}}$

$\purple{\boxed{\bf{Time=\dfrac{Distance}{Speed}}}}$

So,

$\longrightarrow\rm{t_{1}=\dfrac{120}{40}=3h}$

$\longrightarrow\rm{t_{2}=\dfrac{480}{v}}$

Now,

$\longrightarrow\rm{Average\:Speed=\dfrac{Total\:distance\:covered}{Total\:time\:taken}}$

$\longrightarrow\rm{60=\dfrac{600}{t_{1}+t_{2}}}$

$\longrightarrow\rm{\cancel{60}=\dfrac{\cancel{600}}{3+\dfrac{480}{v}}}$

$\longrightarrow\rm{1=\dfrac{10}{\dfrac{3v+480}{v}}}$

$\longrightarrow\rm{1=\dfrac{10v}{3v+480}}$

$\longrightarrow\rm{3v+480=10v}$

$\longrightarrow\rm{480=10v-3v}$

$\longrightarrow\rm{480=7v}$

$\longrightarrow\rm{7v=480}$

$\longrightarrow\rm{v=\dfrac{480}{7}\:Km/h}$

$\longrightarrow\rm\green{v=68.57\:Km/h}$

Therefore, speed of bus for last 480 Km is 480/7 Km/h or 68.57 Km/h

Answer 2

Time taken by bus to travel first 120 km is,

$\longrightarrow\sf{t_1=\dfrac{120}{40}\ h}$

$\longrightarrow\sf{t_1=3\ h}$

Let the speed at which the bus travels next 480 km be v.

Hence the time taken by the bus to travel this 480 km (in hours) is,

$\longrightarrow\sf{t_2=\dfrac{480}{v}}$

We know the expression for average speed,

$\longrightarrow\sf{Average\ speed=\dfrac{Total\ distance}{Total\ Time}}$

Here average speed is $\sf{60\ km\,h^{-1}.}$

$\longrightarrow\sf{\dfrac{600}{t_1+t_2}=60}$

$\longrightarrow\sf{\dfrac{600}{\left(3+\dfrac{480}{v}\right)}=60}$

$\longrightarrow\sf{3+\dfrac{480}{v}=10}$

$\longrightarrow\sf{\dfrac{480}{v}=7}$

$\longrightarrow\sf{\underline{\underline{v=68.57\ km\,h^{-1}}}}$

Hence the bus should cover next 480 km with a speed of $\bf{68.57\ km\,h^{-1}.}$