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???

Answer 1

Answer :-

13km/h

Explanation :-

Given :

A boy runs for 10 min at a uniform speed of 9km/hr and 20 min at average speed of 12km/hr

To Find :

Speed the boy will take in next 20 min = ?

Solution :

We know,

$\sf{}Average\ Speed=\dfrac{Total\ Distance}{Total\ Time}$

Total time => 10 + 20 = 30min

Convert minute into hour.         [1h= 60min,so 1min = 1/60h]

Thus, total time in min = 30/60

$\sf{}\implies 12=\dfrac{Toatl\ distance}{\frac{30}{60}}$

$\sf{}\implies 12\times \dfrac{30}{60}=Total\ distance$

$\sf{}\therefore Total\ distance=6km$

Therefore,total distance is equal 6m

Distance covered in 10min/distance which boy walk earlier) :-

We know,

$\sf{}Speed=\dfrac{Distance}{Time}$

Covert 10 min into hr

=> 10/60hour

$\sf{}\implies 9=\dfrac{Distance}{\frac{10}{60}}$

$\sf{}\implies 9\times \dfrac{10}{60}=Distance$

$\sf{}Distance=1.5km$

Then remaining distance,

$\sf{}\bf{}Remaing\ distance=Total\ distance-distance\ travelled\ earlier$

$\sf{}\implies 6-1.5$

$\sf{}\therefore 4.5km$

Therefore,for next 20 the boy should run with a speed,

$\sf{}Speed=\dfrac{Distance}{Time}$

Covert 20min into hr

=> 20/60hr

$\sf{}Speed=\dfrac{4.5}{\frac{20}{60}}$

$\sf{}\implies \dfrac{4.5}{\frac{2}{6}}$

$\sf{}\implies \dfrac{4.5}{\frac{1}{3}}$

$\sf{}\implies 4.5\div \dfrac{1}{3}$

$\sf{}\implies 4.5\ \times 3$

$\sf{}\therefore 13.5km/h$

Therefore,speed needed for next 20min is equal to 13.km/h

Answer 2

$\huge\bold\red{Solution☑}$

Average speed= 12km/hr

Total time=(10+20) min

=(30)min

=1/2 hr

_____________________________

Speed=$\frac{distance}{time}$

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

D= s*t

=9*1/6 (10 min=1/6 hr)

=3/2 km

find d2

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

6=3/2+ d2

D2=9/2 km

So from (3)

Speed=d2/t2

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

=27/2

=13.5 km/hr

=13.5 km/hr

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That's what i found!