An algebra problem by A Former Brilliant Member

Algebra Level pending

An army officer will deliver a message from A to C. He will travel by car at 80 miles per hour from A to B, and then by airplane to C against a wind blowing 30 miles per hour. The speed of airplane in still air is 250 miles per hour. If the army officer takes 4 hours in going from A to C, and $3$ $\frac{4}{7}$ hours for the return trip, how far is B from C in miles?

The answer is 440.

1 solution

A Former Brilliant Member
Dec 20, 2016

$t=(\frac{d}{V}$ ), where t=time, V=speed, d= distance

from A to C, the total time is 4 hours,

$\frac{AB}{80}$ $+$ $\frac{BC}{220}$ $=$ $4$ ------(1)

from C to A, the total time is $3$ $\frac{4}{7}$ hours,

$\frac{AB}{80}$ $+$ $\frac{BC}{280}$ $=$ $3$ $\frac{4}{7}$ ------(2)

subtract equation (2) from (1), we obtain

$\frac{3 BC}{3080}$ $=$ $\frac{3}{7}$

$BC$ $=$ $440 miles$

An algebra problem by A Former Brilliant Member

The answer is 440.

1 solution

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