World problem

Question

The Iditarod sled dog race extends 1049 miles from Anchorage to Nome. If a musher is four times as far from Anchorage as from Nome, how many miles has the musher completed?

Answer 1

This is a problem with two unknowns, the distance from Anchorage and the distance from Nome. To solve a problem with 2 unknowns you must have 2 equations.

Let x=distance from Anchorage in miles

     y=distance from Nome in miles

Eq. I:  x+y=1049

Eq. II: Because the distance is given that he/she is 4x farther from Anchorage than Nome, we can write

         x=4y

Using the substitution method we can put the value of x=4y from Eq. II into Eq. I and solve for y:

         x+y=1049           Eq. I

        4y+y=1049          substituting 4y for x

        5y=1049              adding like terms

        y=1049/5             divide both sides by 5

        y=209.8

Putting this value for y into Eq. II:

        x=4y           Eq. II

        x=4(209.8)  substitute value for y

        x=839.2      solve for x

Because the race started at Anchorage the distance completed is the distance from there, so the answer is 839.2 miles.