Question

Ramesh travels 760 km to his home partly by train and partly by car. He takes 8 hours if he travels 160 km by train and the rest by car. He takes 12 minutes more if the travels 240 km by train and the rest by car. Find the speed of the train and car respectively.

Answer 1

The speed of car is 100 km/h

The speed of train is 80 km/h

Step-by-step explanation:

Given as :

Total distance cover by Ramesh = D = 760 km

The distance cover by train = $D_1$ = 160 km

The distance cover by car = $D_2$ = 760 - 160 = 600 km

Total time taken = $T_1$ = 8 hours

Let The Speed of train = x km/h

Let The speed of car = y km/h

According to question

Time = $\dfrac{distance}{speed}$

So, 8 = $\dfrac{D_1}{x}$  +  $\dfrac{D_2}{y}$

Or, 8 = $\dfrac{160}{x}$ + $\dfrac{600}{y}$

i.e  1 = $\dfrac{20}{x}$ + $\dfrac{75}{y}$            .......1

Again

The distance cover by train = $D'_1$ = 240 km

The distance cover by car = $D'_2$ = 760 - 240 = 520 km

Total time taken = $T_2$ = 8 hours + 12 min = 8.2 hours

Let The Speed of train = x km/h

Let The speed of car = y km/h

According to question

Time = $\dfrac{distance}{speed}$

So, 8.2 = $\dfrac{D'_1}{x}$  +  $\dfrac{D'_2}{y}$

Or, 8.2 = $\dfrac{240}{x}$ + $\dfrac{520}{y}$                    ......2

Solving eq 1 and eq 2

12 × 1 - 8.2 = 12 ( $\dfrac{20}{x}$ + $\dfrac{75}{y}$  ) - ( $\dfrac{240}{x}$ + $\dfrac{520}{y}$    )

Or, 3.8 = ( $\dfrac{240}{x}$ - $\dfrac{240}{x}$ ) + ( $\dfrac{900}{y}$ - $\dfrac{520}{y}$ )

Or, 3.8 = 0 + $\dfrac{900-520}{y}$

Or, y = $\dfrac{380}{3.8}$

∴    y = 100

So, The speed of car = y = 100 km/h

Put the value of y in eq 1

∵  1 = $\dfrac{20}{x}$ + $\dfrac{75}{y}$

or, 1 = $\dfrac{20}{x}$  +  $\dfrac{75}{100}$

Or, $\dfrac{20}{x}$ = 1 - $\dfrac{75}{100}$

Or, $\dfrac{20}{x}$  = $\dfrac{100- 75}{100}$

Or, $\dfrac{20}{x}$  =  $\dfrac{25}{100}$

∴   20 × 100 = 25 × x

Or,  x = $\dfrac{2000}{25}$ = 80 km/h

So, The speed of train = x = 80 km/h

Hence, The speed of car is 100 km/h

And The speed of train is 80 km/h   Answer