Question

A boy runs for 10 minutes at a uniform speed of 9 km per hour at what speed should he Run for next 20 minutes so that the average speed comes to 12 km per hour which book question is this

Answer 1

Given ->

Average speed = 12 km/hr

Total time = (10 + 20) min

= (30) min

= 1/2 hr

We know ->

Average speed = total distance/total time

= (d1 + d2)/(t1+t2) ....(1)

We have ->

d1 = s*t

= 9*1/6.... {10 min = 1/6 hour}

= 3/2 km..... (2)

Let's find d2 from (1) and (2),

12 = (3/2+d2) /1/2

6 = 3/2 + d2

d2 = 9/2 km.... (3)

So, from (3),

Speed = d2/t2

= (9/2)/(1/3)

= 27/2

= 13.5 km/hr

The Run for next 20 minutes should be at 13.5 km/hr so that the average speed comes to 12 km/hr.

Answer 2

$\bold{\underline{Question:}}$

A boy runs for 10 minutes at a uniform speed of 9 km per hour. At what speed should he Run for next 20 minutes so that the average speed comes to 12 km per hour.

$\bold{\underline{Solution:}}$

$\bold{\underline{\textsf{In 1st case,}}}$

Given :

• Speed = s₁ = 9 km h⁻¹.
• Time = t₁ = 10 min = $\bold{\frac{1}{6}}$ hrs.

$\boxed{\bold{Distance =Speed*Time}}$

So

• D₁ = $\bold{9*\frac{1}{6}=\frac{3}{2}{\quad}km.}$

$\underline{\bold{\textsf{In 2nd Case,}}}$

Given :

• Time = t₂ = 20 min = $\bold{\frac{1}{3}\:hrs.}$
• D₂ = ?
• Speed = s₂ = ?

$\boxed{\bold{Average\:speed=\frac{D_1+D_2}{t_1+t_2}=12\:km\:h^{-1}}}$

$\implies{\bold{\frac{\frac{3}{2}+D_2}{\frac{1}{6}+\frac{1}{3}}=12}}\\\\\\\implies{\bold{\frac{\frac{3+2D_2}{2}}{\frac{1}{2}}=12}}\\\\\\\implies{\bold{3+2D_2=12}}\\\\\\\implies{\bold{2D_2=9}}\\\\\boxed{\bold{D_2=4.5\:km.}}$

So

$\bold{s_2=\frac{D_2}{t_2}=\frac{4.5}{\frac{1}{3}}=4.5*3=13.5\:km\:h^{-1}.}\\\\\\\boxed{\bold{\textsf{Speed to maintain agverage = 13.5 km per hr.}}}$