Far, far away

Algebra Level pending

Kana-chan has an urgent meeting at a faraway place, and has to travel by car from City A to City C in the shortest time possible. She travels from A to B at a (constant) speed of 60 kph, and from B to C at 80 kph, reaching her destination in 8.5 hours. After the meeting, she returns from C to B at 60 kph, and from B to A at 80 kph, taking her 9 hours on the return trip.

In kilometers, how far is City A from City C?

The answer is 600.

1 solution

Jaydee Lucero
Jun 27, 2017

Let $AB$ be the distance from A to B (or from B to A), and $BC$ be the distance from B and C (or from C to B). Since $\mathrm{time=\dfrac{distance}{speed}}$ , the trip from $A\rightarrow B \rightarrow C$ is given by

$\frac{AB}{60}+\frac{BC}{80}=8.5$

while the trip from $C\rightarrow B \rightarrow A$ is given by

$\frac{BC}{60}+\frac{AB}{80}=9$

Solving the equations simultaneously, we obtain $AB=240$ and $BC=360$ , giving $AC=AB+BC=\boxed{\mathrm{600 \ km}}$ .

Far, far away

The answer is 600.

1 solution

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