Question

Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 mph faster than Charlene. They meet in 5 hours. Find Charlene's speed.

Answer 1

34 mph.

Explanation:

Let x be speed of Charlene, then speed of Paul will be x+16 as we are given that Paul is driving 16 mph faster than Charlene.

Let y be distance covered by Charlene, then distance covered by Paul will be 420-y.

Now we will use formula
`\text{Speed}=\frac{\text{Distance}}{\text{Time}}`. Upon using our given information we will get two equation and two unknowns as:

`x+16=(420-y)/(5)...(1)`

`x=(y)/(5)...(2)`

Upon substituting
`x=(y)/(5)` in 1st equation we will get,

`(y)/(5)+16=(420-y)/(5)`

Upon multiplying both sides of our equation by 5 we will get,

`5((y)/(5)+16)=420-y`

`5*(y)/(5)+5* 16=420-y`

`y+80=420-y`

`y+80+y=420-y+y`

`2y+80=420`

`2y=420-80`

`2y=340`

`y=(340)/(2)`

`y=170`

Upon substituting y=170 in 2nd equation we will get,

`x=(170)/(5)`

`x=34`

Therefore, Charlene's speed is 34 miles per hour.