Question

A boy runs for 20 min. at a uniform speed of 18km/h. At what speed should he run for the next 40 min. so that the average speed comes 24km/hr.

Answer 1

Given:-

→ 1st time period = 40 min

→ Speed with which the boy runs first

20 min = 18km/h

→ 2nd time period = 40 min

→ Average speed of the boy = 24km/h

To find:

→ Speed with which, the boy should run

next 40 min to get the required

average speed.

Solution:-

Let the 1st time period be t₁ and let the second time period be t₂ . Also, let the 1st speed be v₁ and the required speed be v₂ .

Firstly, let's convert t₁ and t₂ from minute to hour :-

=> 1min = 1/60 h

=> 20min = 20×(1/60)

=> 1/3 h (t₁)

=> 40min = 40×(1/60)

=> 2/3 h (t₂)

Now, let the distances covered by the boy in both time intervals be d₁ and d₂ .

Distance = Speed × Time

∴ d₁ = v₁t₁

∴ d₂ = v₂t₂

Average speed :-

= Total distance/Total time

=> Vₐᵥ = [d₁ + d₂]/[ t₁ + t₂]

=> Vₐᵥ = [v₁t₁ + v₂t₂]/[t₁ + t₂]

=> 24 = [18×1/3 + v₂×2/3]/[1/3 + 2/3]

=> 24 = [6 + 2v₂/3]/1

=> 24×3 = 18 + 2v₂

=> 72 = 18 + 2v₂

=> 2v₂ = 72 - 18

=> 2v₂ = 54

=> v₂ = 54/2

=> v₂ = 27 km/h

Thus, the boy should run the next 40 min at a speed of 27km/h .

Answer 2

Answer:

Your answer is on the above attachment

Hope this helps you