Question

A cab in NYC charges you $1.25 a mile and a flat fee of $4 to ride in the cab. A cab in Chicago charges you $0.75 a mile but a flat fee of $6 just to get in the cab. If you paid the same amount of money for a cab ride in each city how many miles would the cab have driven you?

Answer 1

After 4 miles driven by cab the amount would be same in both cities.

Explanation:

Let the number of miles be 'x'.

Given:

In NYC

Flat fee of cab = $4

Per mile charge = $1.25

Total cab charges is equal to sum of Flat fee of cab and per mile charge multiplied by number of miles.

Framing in equation form we get;

Total cab charges in NYC =
`4+1.25x`

In Chicago

Flat fee of cab = $6

Per mile charge = $0.75

Total cab charges is equal to sum of Flat fee of cab and per mile charge multiplied by number of miles.

Framing in equation form we get;

Total cab charges in Chicago =
`6+0.75x`

Now we need to find number of miles driven so that the amount could same in both cities.

Total cab charges in NYC = Total cab charges in Chicago

`4+1.25x=6+0.75x`

Combining like terms we get;

`1.25x-0.75x=6-4\\\\0.5x=2`

using Division Property we will divide both side by 0.5 we get;

`(0.5x)/(0.5) =(2)/(0.5) \\\\x=4`

Hence After 4 miles driven by cab the amount would be same in both cities.