# Difference between revisions of "1997 PMWC Problems/Problem I13"

## Problem

A truck moved from $A$ to $B$ at a speed of $50 \text{ km/h}$ and returns from $B$ to $A$ at $70 \text{ km/h}$. It traveled $3$ rounds within $18$ hours. What is the distance between $A$ and $B$?

## Solution

The truck moved from A to B back and forth once in 18/3=6 hours. Let the time that it takes to go from A to B be $T_1$, and let the time it takes to go from B to A be $T_2$.

$T_1+T_2=6$

$50T_1=70T_2\Rightarrow T_1=\frac{7}{5}T_2$

$\frac{12}{5}T_2=6\Rightarrow T_2=\frac{5}{2}$

Therefore the distance from A to B is $\frac{5}{2}\cdot70=\boxed{175}$.