Question

A is twice as fast as B and B is thrice as fast as C is. The journey covered by C in 54 minutes will be covered by B in:

Answer 1

Hint: To solve this question we will have to develop a relation between the speeds of A, B and C. Now, in these relation we will write the speeds of A,B,C in terms of the distance travelled and time taken by A, B and C to cover that distance. This can be achieved by the following formula:
$speed=\dfrac{distance\,travelled}{total\,time\,elapsed}$

Complete step-by-step answer:
In the above question the speeds of A, B and c are not given but the relation between the speeds A, Band c is given. Let us assume that the speed of C is x. Now as given in question, B is thrice as fast as C. so the speed of B will be= 3x. now it is given that A is twice as fast as B. so, the speed of A will be
$=2\left( 3x \right)=6x$
Now, we are given that C travels a fixed distance. Let this distance be denoted by ‘d’. now it is given that this distance is travelled in 54 minutes by C. the relation between the speed of C, the distance travelled by C and the time elapsed is denoted by:
$\begin{align}
  & speed=\dfrac{distance}{time} \\
 & \Rightarrow x=\dfrac{d}{54} \\
 & \Rightarrow d=54x................(i) \\
 & \\
\end{align}$
Now, it is given that B also travels the distance d. Let the time taken by B is denoted by T (in minutes). Now the relation of the speed, distance travelled and time elapsed for B is given by:
$\begin{align}
  & speed=\dfrac{distance\,travelled}{total\,time\,elapsed} \\
 & \Rightarrow 3x=\dfrac{d}{54} \\
 & \Rightarrow T-\dfrac{d}{3x}.........(ii) \\
 & \\
\end{align}$
Now, we will put the value of distance ‘d’ from equation(i) into equation (ii). After doing this, we will get the following results:
$\begin{align}
  & \Rightarrow T=\dfrac{54x}{3x} \\
 & \Rightarrow T=18 \\
\end{align}$
Hence, the time taken by B to cover the same distance as C is 18 minutes.

Note: The time elapsed is also calculated as follows: speed is inversely proportional to time, so if the speed is increased to k times then time is reduced by k.