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The distance between point $A$ and point $B$ is $480$ km. A truck left point $A$ to point $B$, and at the same time a taxi left from point $B$ to point $A$. The two vehicles are moving at a constant rate towards each other and they meet $4$ hours later. If the speed of the taxi is $2$ times the speed of the truck, what is the speed of the truck and the taxi?

Can someone explain to me how to solve this type of problem.

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2 Answers 2

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Hints:

  1. If you know the rate of one, you know the rate of the other.

  2. You don't know either rate, so make up a variable to stand for one of them so you can make mathematical statements about the rates (and note that by (1) above you can express the other rate in terms of that variable too).

  3. Having an expression now for both rates, and knowing the times of travel for both, what is the distance traveled by each (in terms of their rates and times)?

  4. How are the distances related? This will give an equation to solve for the rate variable you created in (2) above.

  5. Knowing one of the rates, you can now state the other rate.


The underlying relationship to ALL problems of this sort is the fundamental idea $$T\times R = D$$ (or, equivalently, $R=D/T$ which I find easier to remember -- think kph = kilometers/hours).

The idea is generally to use two of the quantities ($T$, $R$, or $D$) to find the third one. If you only are told one of them as a number, then you will have to make up a symbol (variable) to stand for one of the others so you actually have something to use for it in that relationship.

It often helps to write an equation in words to roughly describe what you know. There may be more than one. For example, $$(\textrm{taxi rate kph}) = 2\times(\textrm{truck rate kph})$$ and $$(\textrm{taxi distance km}) + (\textrm{truck distance km}) = 480$$ Use known values and/or your variable expressions to "mathematize" these rough equations.

Be methodical. It makes the process easier.

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Let x be the speed of truck. Answer the following questions:

  1. What is the speed of taxi?

  2. What is the sum of taxi and truck speed.

  3. Let's say we have a super-truck with speed equals sum from p.2 and it starts from A towards B. How much time needed for super-truck to come to B.

  4. What is the speed of super-truck

  5. What is the speed of truck

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