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
B
30 miles
C
120 miles
D
200 miles
E
24 miles

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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