Question

Vandana takes 24 minutes to reach her school if she goes at a speed of 5km/h. If she wants to reach the school in 20 minutes , what should be her speed?

Answer 1

Hint: The time dimensions given here are in minutes and the speed is given in km/hr. So, convert the times given into hours so that all the quantities are in the same units. Use the point that distance is the same in both cases. So, equate the distances in both the cases to get the unknown value. We know that the formula for the distance is speed$ \times $(time taken to travel that distance).

Complete step by step answer:
Given that it takes 24 minutes to reach her school at a speed of 5km/h,
Now, converting the time taken into hours we get,
Time taken = $\dfrac{{24}}{{60}} = \dfrac{2}{5}hrs$
Let us suppose that the distance is d;
$ \Rightarrow $Distance to be travelled by vandana to reach her school(d)= speed$ \times $(time taken to travel that distance).
$ \Rightarrow $d=5km/h$ \times \dfrac{2}{5}h$=2 km
Now taking the next case ; it is said that it takes 20 minutes to reach the school;
Now, converting the time taken into hours we get,
Time taken = $\dfrac{{20}}{{60}} = \dfrac{1}{3}hrs$
Let us suppose the speed that she should maintain to reach her school in 20 minutes is s;
$ \Rightarrow $Distance to be travelled by vandana to reach her school(d)= speed$ \times $(time taken to travel that distance).
$ \Rightarrow $d=s$ \times \dfrac{1}{3}h$
We got that d=2 km
$ \Rightarrow $2km=s$ \times \dfrac{1}{3}h$
$ \Rightarrow $s=6 km/h
Which implies the speed required to be maintained by vandana to reach her school in 20 minutes is 6km/h.

Note:
Make sure to change all the dimensions into the same units so that you get an appropriate answer. You can also try this problem by changing all the units to m/sec i.e. converting the times given into seconds and speed into m/sec , then you will also get speed in m/sec as the answer .