Chapter A.8, Problem 52AYU

To determine

To find: How fast is each cyclist riding?

Answer to Problem 52AYU

Cycle riding is 23 miles fast.

Explanation of Solution

Given:

Two cyclists leave a city a city at the same time, one going east and the other going west. The westbound cyclist bikes 5 mph faster than the eastbound cyclist. After 6 hours they are 246 miles apart.

Calculation:

West bound:

Rate $=x+5$ mph; time $=6$ hours; distance $=6\left(x+5\right)=6x+30$ miles.

East bound:

Rate $=x$ mph; time $=6$ hours; distance $=6x$ miles.

Equation:

Distance $+$ Distance $=246$ miles

$6x+30+6x=246$

$12x=216$

$x=18$

Therefore $x+5=23$ mph.