# A boy runs for 10 min. at a uniform speed of 9 km/hr. At what speed should he run for the next 20 min. so that the average speed comes 12 km/hr?

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by MeeraQT

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by MeeraQT

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D1 + D2 / T1 + T2

Total Time = 10 min + 20 min = 30 min =

D1 = Speed * Time = 9 * 1/6 (10 min = 1/6 hr)

= 3/2 km =

D2 = ?

12 = 1.5 + D2 / 1/2

12 * 1/2 = 1.5 + D2

6 = 1.5 + D2

6 - 1.5 = D2

Speed = Distance / Time

= 4.5 / 1/3 (20 min = 1/3 hr)

= 4.5 * 3 (Reciprocal)

=

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Let us solve this in a different way.

Boy runs for first 10 min at 9 kmph = 9 km/hr

Let boy run for next 10 min at V kmph

let boy run for next 10 min at V kmph

His average speed is average of above three.

Average speed = (9+ 2 V) / 3 = 12 kmph

So 9 + 2 V = 3 * 12 = 36

2 V = 36 - 9 = 27

__V = 27/2 = 13.5 km/hr__

Boy runs for first 10 min at 9 kmph = 9 km/hr

Let boy run for next 10 min at V kmph

let boy run for next 10 min at V kmph

His average speed is average of above three.

Average speed = (9+ 2 V) / 3 = 12 kmph

So 9 + 2 V = 3 * 12 = 36

2 V = 36 - 9 = 27