Driver A charges $25 fees and $0.10 per extra mile driven. Driver B charges no fees but charges $0.60 per mile driven. Find the Application distance in miles for which the two drivers will cost the same money. Also, find the cost.

The correct answer is: For a distance of 50 miles, the cost charged by both the drivers will be the same. Also, the cost charged for 50 miles by both the drivers will be $30.

Step-by-step solution:-
Let x be the number of miles driven and y be the total fees charged.
We know that-
Extra charges = Number of miles driven × Rate per mile
∴ Extra charges = x * rate per mile ..................................................... (Equation i)
Now, for Driver A-
Total fees charged = y = Constant fees + Extra charges
∴ Total fees charged = y = Constant fees + x × rate per mile ................... (From Equation i)
∴ Total fees charged = y = 25 + x * 0.10 .................................................... (From given information)
∴ Total fees charged = y = 25 + 0.10 x ....................................................... (Equation ii)
For Driver B-
Total fees charged = y = Constant fees + Extra charges
∴ Total fees charged = y = Constant fees + x × rate per mile ................... (From Equation i)
∴ Total fees charged = y = 0 + x × 0.60 .................................................... (From given information)
∴ Total fees charged = y = 0.60 x ....................................................... (Equation iii)
Since we need to find the distance for which cost of both drivers is the same-
Equating Equations ii & iii, we get-
25 + 0.10 x = 0.60 x
∴ 25 = 0.60 x - 0.10 x
∴ 25 = 0.50 x
∴ 25 / 0.50 = x ...................................................................................... (Dividing both sides by 0.50)
∴ 50 = x
For a distance of 50 miles, the cost charged by both the drivers will be the sam.
Now, at 50 miles i.e. x = 50,
y = 0.60 x ….............................................. (Using Equation iii)
∴ y = 0.60 × 50
∴ y = 30
Note:-
Alternatively, we can find the total cost by using Equation ii,
y = 25 + 0.10 x
∴ y = 25 + 0.10 × 50
∴ y = 25 + 5
∴ y = 30.
Hence, the answer remains the same.