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Question

By car John travelled from city $$A$$ to city $$B$$ in $$3$$ hours . At a rate that was $$20$$ mph higher than John's, Peter cover the same distance in $$2$$ hours. Find the distance between two cities.


A
20 miles
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B
30 miles
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C
120 miles
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D
200 miles
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E
24 miles
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Solution

The correct option is C $$120 \ miles$$
Let the distance between city A and city B be d miles.
For John: $$Speed=\dfrac { Distance }{ Time } =\dfrac { d }{ 3 } mph$$
For Peter: Speed of Peter's car$$=$$Speed of John's car $$+ 20$$mph
$$\Rightarrow \dfrac { d }{ 2 } =\dfrac { d }{ 3 } +20\\ \Rightarrow \dfrac { d }{ 2 } -\dfrac { d }{ 3 } =20\\ \Rightarrow \dfrac { 3d-2d }{ 6 } =20\\ \Rightarrow d=20\times 6=120\\ \Rightarrow d=120miles$$

Physics

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