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. $20miles$
• B. $30miles$
• C. $120miles$
• D. $200miles$
• E. $24miles$

Answer 1

The correct option is C $120miles$

Let the distance between city A and city B be d miles.

For John: $Speed=\frac{Distance}{Time}=\frac{d}{3}mph$

For Peter: Speed of Peter's car$=$Speed of John's car $+20$mph

$\Rightarrow \frac{d}{2}=\frac{d}{3}+20\Rightarrow \frac{d}{2}-\frac{d}{3}=20\Rightarrow \frac{3d-2d}{6}=20\Rightarrow d=20\times 6=120\Rightarrow d=120miles$