Question

16. Nelson travels 600km to her home partly by train and partly by bus. She takes 8 hours if
she travels 120 km by train and the remaining by bus. If she travels 200km by train and
the remaining by bus, she takes 20 minutes longer. Find the speed of the train and the bus seperately
pls fInd it soon please​

Answer 1

Given:

Nelson travels 600km to her home partly by train and partly by bus.

She takes 8 hours if  she travels 120 km by train and the remaining by bus.

If she travels 200km by train and  the remaining by bus, she takes 20 minutes longer.

To find:

The speed of the train and the bus separately.

Solution:

Let's assume,  

" $\bold{S_T}$ " → speed of the train

" $\bold{S_B}$ " → speed of the bus

We know,

$\boxed{\bold{Time = \frac{Distance}{Speed} }}$

So, according to the first part of the question, we can form an equation as,

 $\frac{120}{S_T} + \frac{600 - 120}{S_B} = 8$

$\implies \frac{120}{S_T} + \frac{480}{S_B} = 8$

$\implies 120S_B + 480 S_T = 8 S_T S_B$

on dividing by 8 throughout

$\implies 15S_B + 60 S_T = S_T S_B$ ..... (i)

Again, according to the second part of the question, we can form an equation as,

   $\frac{200}{S_T} + \frac{600 - 200}{S_B} = 8\frac{20}{60}$

$\implies \frac{200}{S_T} + \frac{400}{S_B} = \frac{25}{3}$

on dividing by  $\frac{25}{3}$ throughout

$\implies \frac{24}{S_T} + \frac{48}{S_B} = 1$

$\implies 24S_B + 48 S_T = S_T S_B$

on substituting from (i)

$\implies 24S_B + 48 S_T = 15S_B + 60 S_T$

$\implies 9S_B = 12S_T$

$\implies S_B = \frac{12}{9} S_T$

$\implies S_B = \frac{4}{3} S_T$ .... (ii)

 

 Now, on substituting (ii) in (i), we get  

 $(15\times \frac{4}{3} S_T) + 60 S_T = S_T ( \frac{4}{3} S_T)$

$\implies 20S_T+ 60 S_T = \frac{4}{3} S_T^2$

$\implies 80S_T = \frac{4}{3} S_T^2$

$\implies S_T = \frac{80\times 3}{4}$

$\implies \bold{S_T = 60\:km/hr}$

On substituting the value of $S_T$ in (ii), we get

∴ $S_B = \frac{4}{3} \times 60 = 4 \times 20 = 80\:km/hr$  

Thus,

The speed of the train is → 60 km/hr

The speed of the bus is → 80 km/hr

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