Question

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

Answer 1

Given that, a boy runs for 20 min at a uniform speed of 18 km/h.

Time = 20 min = 20/60 = 1/3 hours

Speed = 18 km/hr

We know that,

Distance = Speed × Time

= 18 × 1/3 = 6 km

We have to find that at what speed should he run for the next 40 min.

Now,

New Time = 40 min = 40/60 = 2/3 hours

New Speed = 24 km/hr

Let us assume that the distance he travelled in 40 min be is x km.

Total distance: x + 6 = 24, x = 24 - 6 = 18 km

Also, assume that he require speed of y km/hr.

Distance = Speed × Time

→ 18 = y × 2/3

→ 18 × 3/2 = y

→ 9 × 3 = y

→ 27 = y

Therefore, the speed of the boys is 27 km/hr.

Answer 2

Given :-

• A boy runs for 20 min.at a uniform speed of 18m/h.
• Total Average speed = 24km/h.

To Find :-

• .At what speed should he run for the next 40 min. ?

Solution :-

Case 1 :-

→ Time = 20 min = (20/60) = (1/3) Hours.

→ Speed = 18km/h.

→ Distance Covered = S * T = 18 * (1/3) = 6km.

Case 2 :-

→ Time = 40 min. = (40/60) = (2/3) Hours.

→ Speed = Let x km/h.

→ Distance Covered = S * T = (2/3) * x = (2x/3) km .

From Both Case we get :-

→ Total Distance covered = (2x/3) + 6 = (2x + 18)/ 3 km.

→ Total Time = 20min. + 40 min. = 60min. = 1 Hour.

So,

→ Average Speed = (Total Distance ) / (Total Time).

→ 24 = [{(2x + 18)/3} / 1 ]

→ 24 = (2x + 18)/3

→ 2x + 18 = 24* 3

→ 2x = 72 - 18

→ 2x = 54

→ x = 27km/h.

Hence, The Boy should Run at a speed of 27km/h for the next 40 minutes.