Question

A man travels 600km apart by train and partly by car. It takes 8 hours and 40 minutes if he travels 320 km by train and rest by car. It would take 30 minutes more if he travels 200 km by train and the rest by the car/. Find the speed of the train and by car separately.

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Answer 1

Answer:

refers to attachment.

Step-by-step explanation:

hope it helps you☆

Answer 2

Step-by-step explanation:

Given:

A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and the rest by car, he takes half an hour longer.

To Find

The speed of the train and car respectively.

Solution:

Total distance =600 km.

Let the speed of the train be x km/hr and the speed of the car be y km/hr.

We know that,

$\star\bf \: Time = Speed \div Distance$

Case 1

$\begin{gathered} \tt \: Time \: taken =\frac{400}{x}+\frac{600-400}{y} \\ \\ \tt\Rightarrow \frac{400}{x}+\frac{200}{y}=6+\frac{30}{60} \\ \tt\Rightarrow\frac{400}{x}+\frac{200}{y}=6+\frac{1}{2} \\ \tt\Rightarrow \frac{400}{x}+\frac{200}{y}=\frac{2\times6+1}{2} \\ \tt\Rightarrow \frac{400}{x}+\frac{200}{y}=\frac{13}{2}...(i) \\ \end{gathered}$

Case 2

Time taken = 6 hours 30 minutes + 30 minutes

=7 hours

$\begin{gathered} \tt \: Time \: taken =\frac{200}{x}+\frac{600-200}{y} \\ \\\tt\Rightarrow \frac{200}{x}+\frac{400}{y}=7...(ii) \\ \\ \tt \: Multiplying \: equation \: (i)\:by 2 \: , we \: get, \\\tt2(\frac{400}{x}+\frac{200}{y})=2(\frac{13}{2}) \\ \tt\frac{800}{x}+\frac{400}{y}=13...(iii) \\ \end{gathered} </p><p>$

Now ,

Subtracting equation (ii) from (iii), we get,

800/x+ 400/y - 200/x - 400/y =13-7 800-200/x =6

600 /x=6

x=600/6

x=60

Now ,

Substituting equation (ii),

we get,

$\begin{gathered} \tt\frac{200}{100}+\frac{400}{y}=7 \\ \tt \: 2+\frac{400}{y}=7 \\ \tt\frac{400}{y}=7-2=5 \\ \tt \: y=\frac{400}{5} \\ \tt \: y=80 \\ \end{gathered}$

$\bf \red{ \bigstar Therefore \: the \: speed \: of \: the \: train \: is \: 10km/hr }\:\\ \bf \red{ and \: the \: speed \: of \: the \: car \: is \: 80 km/hr \: respectively.}$

Hope it helps you lil sister ✌️