Exercise 3.10

Places A and B are $80km$ apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in $8hr$ and if they move in opposite directions, they meet in $1hr20min$. Find the speeds of the cars.

Let the speed of the car leaving A to be 'x' km/h and the speed of the car leaving B to be 'y' km/h. Total distance=80 km Also 1 hour 20 mins= 4/3 hour When an automobile goes in the same direction...

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A woman travels $600km$ partly by train and partly by car. If he covers the $400km$ by train and the rest by car, it takes him $6hr$ and $30min$. But, if he travels $200km$ by train and the rest by car, he takes half an hour longer. Find the speed of the train and the speed of the car.

Let’s suppose speed of the train be $Akm/hr$ speed of the car $=Bkm/hr$ There are two parts Part 1: When the women travels $400km$ by train and the rest by car. Part 2: When Riya travels $200km$ by...

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

Let’s assume, The speed of the train be $Ckm/hr$ The speed of the car $=Dkm/hr$ From the question, it’s understood that there are two parts # Part 1: When Ramesh travels $160Km$ by train and the...

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A man walks a certain distance with a certain speed. If he walks $1/2km$ an hour faster, he takes 1 hour less. But, if he walks 1km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

Let the actual speed of the man be $Ckm/hr$ and D be the actual time taken by him in hours. So, we know that Distance covered = speed C distance ⇒ Distance$=C\times D=CD$ …………………………. (i) First...

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The boat goes $30km$ upstream and $44km$ downstream in $10$ hours. In $13$ hours, it can go $40km$ upstream and $55km$ downstream. Determine the speed of the stream and that of the boat in still water.

Let’s assume, The speed of the boat in still water as $Ckm/hr$ And, The speed of the stream as $Dkm/hr$ We know that, Speed of the boat in upstream $=(C–D)km/hr$ Speed of the boat in downstream...

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Points A and B are $70km$. apart on a highway. P car starts from P and another car starts from B simultaneously. If the D travel in the same direction, the D meet in $7hrs$, but if the D travel towards each other, the D meet in one hour. Find the speed of two cars.

Let’s consider the car starting from point P as C and its speed as C km/hr. The car starts from point B as D and its speed as D km/hr. There are two cases in the question: Case i: Car C and D are...

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