Question

Payal can cover a certain distance in 1 hour 24 minutes by covering two – thirds of the distance at 4 km/hr and the rest at 5 km/hr. Find the total distance.
(a) 2 km
(b) 4 km
(c) 8 km
(d) 6 km

Answer 1

Hint: Assume the total distance travelled by Payal as d km. Consider that she takes ${{t}_{1}}$ hours in travelling two – thirds of the distance and time ${{t}_{2}}$ hours in travelling the remaining one – third of the distance. Take the sum of ${{t}_{1}}$ and ${{t}_{2}}$ and equate it with 1 hour 24 minutes after converting the minutes into hours by using the relation 1 hour = 60 minutes. Now, apply the formula of time = $\dfrac{\text{distance}}{\text{speed}}$ and substitute the given value of speeds for the two assumed times and calculate the value of d.

Complete step-by-step solution:
Here we have been provided with the information regarding the journey of Payal in two parts. We have to determine the total distance travelled by Payal in 1 hours 24 minutes. Let us consider the two parts separately.
Now, let us assume that the total distance travelled Payal is d km.
(1) It is given that she travels two – thirds of the total distance with a speed of 4 km/hr. Assuming that she takes time ${{t}_{1}}$ hours while covering this distance we have,
Speed = 4 km/hr, distance = $\dfrac{2}{3}d$ km and time take = ${{t}_{1}}$ hours, therefore using the formula: - time = $\dfrac{\text{distance}}{\text{speed}}$ we get,
$\begin{align}
  & \Rightarrow {{t}_{1}}=\dfrac{2d}{3\times 4} \\
 & \Rightarrow {{t}_{1}}=\dfrac{d}{6}.............\left( i \right) \\
\end{align}$
(2) Now, in the second part of the journey it is said that she travels the remaining distance with a speed of 5 km/hr. Considering that she takes time ${{t}_{2}}$ hours while covering this distance we have,
Speed = 5 km/hr, distance = $\dfrac{1}{3}d$ km and time take = ${{t}_{2}}$ hours, therefore again using the formula: - time = $\dfrac{\text{distance}}{\text{speed}}$ we get,
$\begin{align}
  & \Rightarrow {{t}_{2}}=\dfrac{d}{3\times 5} \\
 & \Rightarrow {{t}_{2}}=\dfrac{d}{15}.............\left( ii \right) \\
\end{align}$
Now, it is said that she take 1 hour 24 minutes to travel the total distance that means we must have: -
$\Rightarrow {{t}_{1}}+{{t}_{2}}=$ 1 hour 24 minutes
Converting minutes into hours by using the relation 1 hour = 60 minutes and substituting the values of times using equations (i) and (ii) we get,
$\begin{align}
  & \Rightarrow \dfrac{d}{6}+\dfrac{d}{15}=1+\dfrac{24}{60} \\
 & \Rightarrow \dfrac{7d}{30}=\dfrac{7}{5} \\
 & \therefore d=6km \\
\end{align}$
Hence, option (d) is the correct answer.

Note: Note that you must convert all the quantities into one unit otherwise there may occur some calculation mistake. Here we converted the total time in hours because the speed was provided in km/hr so it is of no sense to convert them in minutes and increase the calculation. You must remember the speed – time formula to solve the above question.