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

Average speed$=\frac{total\ distance}{total\ time\ taken}$

$t_1=20\ min=\frac{20}{60}\ h=\frac{1}{3}\ h$   [1 hour=60 minutes]

Then, the distance travelled in $20\ min=speed\times time=\frac{18}{3}=6\ km$

Let  '$x$' km be the distance travelled in another $40$ minutes.

$t_2=40\ min=\frac{40}{60}=\frac{2}{3}\ h$ 
 
Total distance $=( 6+x)\ km$

Total time taken$=( \frac{1}{3})+( \frac{2}{3})=1\ h$
 
On substituting these values in

$24=6+x$

$x=24-6=18\ km$

Thus, the distance travelled by the boy in $40\ min$ is $18\ km.$
 
Using this we can calculate the speed at which boy must run in another $40\ min$

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

Speed$=\frac{18}{( \frac{2}{3})}=\frac{( 18\times3)}{2}=27\ km/h$
 
There, the boy must run with speed of $27\ km/h$ so that his average speed becomes $24\ km/h$ .
 

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Updated on: 10-Oct-2022

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