Question

A man travels 400 km partly by train and partly by car. If he covers half the distance by train and the rest by car, it takes him 4 hours 30 minutes. But if he travels 100km by train and rest by car, he takes 15 minutes longer. Find the speed of the train and that of the car.

Answer 1

$$\textbf{Step 1 : Make eq. from given information.}$$

$$\text{Let , the speed of train = x km/hr and}$$

$$\text{the speed of car = y km/hr}$$

$$\dfrac{200}{x}+\dfrac{400-200}{y}=4hr. 30 min$$

$$\Rightarrow$$ $$\dfrac{200}{x}+\dfrac{200}{y}=4.5 hr......................(1 min= \dfrac{1}{60}hr)........(i)$$

$$\dfrac{100}{x}+\dfrac{400-100}{y}=4hr. 30 min +15min$$

$$\Rightarrow$$ $$\dfrac{100}{x}+\dfrac{300}{y}=4.75 hr$$

$$\Rightarrow$$ $$\dfrac{200}{x}+\dfrac{600}{y}=9.5 hr.....................(multiply \ 2)......(ii)$$

$$\textbf{Step 2 : Solving equation (i) & (ii).}$$

$$\text{Substitute }{\dfrac{1}{x}=m } \ and \ {\dfrac{1}{y}= n}$$

$$\text{we get,}{200m + 200n=4.5}............(iii)$$

$${200m + 600n=9.5}............(iv)$$

$$\text{subtract (iv)-(iii)} $$

$$\text{we get ,} {n = \dfrac{1}{80}}$$

$$\text{and} \ {m = \dfrac{1}{100}}.........................{\text{(put value n in eq. (iii))}}$$

$$\textbf{Step 3 : Finding x & y}$$

$$\text{Resubstitute} \ {x=\dfrac{1}{m} , y=\dfrac{1}{n}}$$

$$\Rightarrow x = 100 \ and \ y = 80$$

$$\textbf{Hence, Speed of train and car is 100 km/hr & 80 km/hr resp.}$$