Question

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

Answer 1

Let $x$ be John's rate in travelling between the two cities.

The rate of Peter will be $x+10$.

We use the rate-time-distance formula to write the distance $D$ travelled by John and Peter (same distance $D$)

$D=3x$ .....(i) and $D=2(x+20)$ ......(ii)

The first equation can be solved for $x$ to give

$x=\frac{D}{3}$

Substitute $x$ by $\frac{D}{3}$ into the second equation

$D=2(\frac{D}{3}+20)$

Solve for $D$ to obtain $D=120$ miles .