Question

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

Answer 1

Hint: Speed is calculated as distance/ time which means distance=speed × time. In the both cases given in the question, distance is the same but speed and time will change. Using the speed and time from the first case find distance to school. Using the obtained distance from the first case and the speed given in the second case, find the speed required in the second case.


Complete step-by-step Solution:
We are given that Vandana takes 24 minutes to reach her school if she goes at a speed of 5km/hour.
We have to find the speed if she wants to reach her school in 20 minutes.
In the first case,
$
  Speed = \dfrac{{dist}}{{time}} \\
  Dist = Speed \times time \\
 $
Speed=5km/hr, time=24minutes
$
  dist = 5\dfrac{{km}}{{hr}} \times 24\min \\
  1hr = 60\min \\
  1\dfrac{{km}}{{hr}} = \dfrac{1}{{60}}\dfrac{{km}}{{\min }} \\
  dist = 5 \times \dfrac{1}{{60}}\dfrac{{km}}{{\min }} \times 24\min \\
   = \dfrac{{5 \times 24}}{{60}}km \\
   = 2km \\
 $
Therefore, the distance to school is 2km.
In the second case,
 $Speed = \dfrac{{dist}}{{time}}$
Distance=2km, time=20 minutes, speed=?
$
  Speed = \dfrac{{dist}}{{time}} \\
  Speed = \dfrac{{2km}}{{20\min }} \\
  1hr = 60\min \\
  1\min = \dfrac{1}{{60}}hr \\
  20\min = \dfrac{{20}}{{60}}hr = \dfrac{1}{3}hr \\
  Speed = \dfrac{{2km}}{{\left( {\dfrac{1}{3}hr} \right)}} \\
  Speed = 2 \times 3\dfrac{{km}}{{hr}} \\
  Speed = 6\dfrac{{km}}{{hr}} \\
 $
Therefore, to reach the school in 20 minutes Vandana has to go at a speed of 6km/hr.


Note: Another approach to solve the above question:
The distance to the school is the same in both cases which is ‘d’, speeds are s1, s2 and times are t1, t2.
In the first case, distance 1 = speed × time which is s1 × t1
In the second case, distance 2= speed × time which is s2× t2
Distance1=distance2=d
$s1 \times t1 = s2 \times t2$
S1=5km/hr, t1=24min, t2=20min, s2=?
$
  s1 \times t1 = s2 \times t2 \\
  5 \times 24 = s2 \times 20 \\
  s2 = \dfrac{{5 \times 24}}{{20}} \\
  s2 = \dfrac{{120}}{{20}} \\
  s2 = 6km/hr \\
 $
Therefore, 6km/hr speed is required by Vandana to reach the school in 20 minutes.