Maths-
General
Easy

Question

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.

hintHint:

1. Extra charges = number of miles driven × rate per mile
2. Total cost = Constant fees + Extra charges.

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.

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