Each week Dan drives two routes, route X and route Y - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

Let the length of route X be denoted as $x$ miles and the length of route Y as $y$ miles.

From the first scenario, we have the equation: $3x + 2y = 134$

From the second scenario, we have the equation: $2x + 5y = 203$

To solve these equations, we can use the substitution or elimination method. Let's use the elimination method.

Multiply the first equation by 5: $15x + 10y = 670$

Multiply the second equation by 2: $4x + 10y = 406$

Now, subtract the second equation from the first: $15x + 10y - (4x + 10y) = 670 - 406$ This simplifies to: $11x = 264$

Solving for $x$, we get: $x = \frac{264}{11} = 24$

Now, substituting $x = 24$ back into one of the original equations to find $y$. We'll use the first equation: $3(24) + 2y = 134$ $72 + 2y = 134$ $2y = 134 - 72$ $2y = 62$ $y = \frac{62}{2} = 31$

Therefore, the lengths of the routes are:

• Route X = 24 miles
• Route Y = 31 miles