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.

Hint:

### 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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