Question

Question #30618

Answer 1

#{: (J=2R), (J+R=120) ]# or combine as a single `2R+R=120`

Answer 2

Rachel: `40` miles

James: `80` miles

Explanation:

"James drove twice as far as Rachel".

This statement can be algebraically expressed as:

`Rightarrow J = 2 R`

"Altogether they drove `120` miles".

`Rightarrow J + R = 120` `"miles"`

Let's substitute the first equation into the second equation:

`Rightarrow (2 R) + R = 120` `"miles"`

`Rightarrow 3 R = 120` `"miles"`

`therefore R = 40` `"miles"`

We now know that Rachel drove for a total of `40` miles.

Let's substitute this value into the first equation to find out how many miles James drove:

`Rightarrow J = 2 (40)` `"miles"`

`therefore J = 80` `"miles"`

James drove for a total of `80` miles.