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 $\frac{5}{2}\cdot70=\boxed{175}$ .

1997 PMWC (Problems)
Preceded by Problem I12	Followed by Problem I14
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10

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1997 PMWC Problems/Problem I13

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