# Thread: Algebra speed problem

1. ## 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.

2. 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
$v - V = \frac{48}{6} = 8$

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

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

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

$2v - 16 = 8$

$v = 12~mph$

-Dan