# Algebra speed problem

• May 20th 2008, 03:01 PM
sp0rtskid55
Algebra speed problem
It took a cyclist 6 h to travel 48 mi going against the wind. The next day on the return trip, it took the cyclist 3 h traveling with the wind. What was the speed of the cyclist?

Also they say i need to make some chart so if you know of any charts to solve this problem please post them.
• May 20th 2008, 04:38 PM
topsquark
Quote:

Originally Posted by sp0rtskid55
It took a cyclist 6 h to travel 48 mi going against the wind. The next day on the return trip, it took the cyclist 3 h traveling with the wind. What was the speed of the cyclist?

Also they say i need to make some chart so if you know of any charts to solve this problem please post them.

Say the speed of the wind is V (in mph). If the cyclist's speed without the wind is v (in mph), then we know that the cyclist's speed with the wind is v + V and against it is v - V. So
$\displaystyle v - V = \frac{48}{6} = 8$

and
$\displaystyle v + V = \frac{48}{3} = 16$

Solving the bottom equation for V:
$\displaystyle V = 16 - v$

and inserting this value of V into the top equation:
$\displaystyle v - (16 - v) = 8$

$\displaystyle 2v - 16 = 8$

$\displaystyle v = 12~mph$

-Dan