Question

One taxi charges a fixed fee of $5 plus $0.45 per mile. Another taxi does not charge a fixed fee, and the rate per mile is $1.70. For how many miles would the cost for each taxi service be the same?

Answer 1

To determine at what distance the cost for both taxi services will be equal, we'll have to establish an equation and solve it.

Let's denote the cost of the first taxi service as cost1 and the cost of the second taxi service as cost2. We let the distance in miles be represented by the variable 'miles'.

First, let's write down the cost for each taxi service for a certain distance:

- cost1 = $5 (fixed fee) + $0.45 * miles (rate per mile)
- cost2 = $1.7 * miles (rate per mile)

We want to find out for how many miles the cost for each taxi service would be the same. This means cost1 = cost2, so we set up the equation:

$5 + $0.45 * miles = $1.7 * miles

To find 'miles', we need to isolate it. First, we can subtract $0.45 * miles from both sides of the equation:

$5 = $1.7 * miles - $0.45 * miles

This simplifies to:

$5 = $1.25 * miles

Then we solve for 'miles' by dividing both sides by $1.25:

miles = $5 / $1.25

This gives us:

miles = 4

So, for 4 miles, the cost for each taxi service would be the same.