Question

While planning a vacation to Europe, Cal wanted to go to Dublin, Ireland, London, England and Paris, France. The distance from Dublin to London is 78 more miles than the distance between London and Paris. If the distance between Dublin and Paris is 504 miles, including the stop in London, what is the distance between London and Paris? What is the distance between Dublin and London?

Please show your work!

Answer 1

The distance between London and Paris is 213 miles, and the distance between Dublin and London is 291 miles.

Explanation:

Let's assign variables to the unknown distances:

Distance from London to Paris = x

Distance from Dublin to London = x + 78

According to the given information, the distance between Dublin and Paris, including the stop in London, is 504 miles. Using these values, we can set up the equation:

Distance from Dublin to London + Distance from London to Paris = 504

(x + 78) + x = 504

Combining like terms:

2x + 78 = 504

Subtracting 78 from both sides:

2x = 426

Dividing both sides by 2:

x = 213

Therefore, the distance between London and Paris is 213 miles, and the distance between Dublin and London is 213 + 78 = 291 miles.

Answer 2

291

Explanation:

Think of a triangle with vertices D (Dublin), L (London), and P (Paris).

Let x = DL

Let y = LP

Let z = DP

"The distance from Dublin to London is 78 more miles than the distance between London and Paris."

DL = LP + 78

x = y + 78

If the distance between Dublin and Paris is 504 miles, including the stop in London.

DL + LP = 504

x + y = 504

x = y + 78

x + y = 504

y + 78 + y = 504

2y = 426

y = 213

x = y + 78

x = 213 + 78

x = 291