Answer: \(3\dfrac{3}{4}\text{ hours}\)
Step-by-step explanation:
Let x denotes the number of hours to cover the entire distance between these two cities .
Using formula \(\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}\), we have
\(\text{Speed}=\dfrac{1}{x}\) (1)
Given : A train traveled \(\dfrac{1}{5}\) of the distance between two cities in \(\dfrac{3}{4}\) hour.
Then,
\(\text{Speed}=\dfrac{\dfrac{1}{5}}{\dfrac{3}{4}}=\dfrac{1}{5}\times\dfrac{4}{3}=\dfrac{4}{15}\) (2)
From (1) and (2), we have
\(\dfrac{4}{15}=\dfrac{1}{x}\\\\\Rightarrow\ x=\dfrac{15}{4}=3\dfrac{3}{4}\text{ hours}\)
Hence, it will take \(3\dfrac{3}{4}\text{ hours}\) to complete the entire distance between these two cities.
