Maria bikes 25 km per hour and starts at mile 10. Glen bikes 29 km per hour and starts at mile 0. Which system of linear equations represents this situation?

Question

A. Maria: d = 251 + 10
Glen. d = 291
B. Glen. d = 25г + 10
Maria: d = 29r
C. Maria: d = 101 + 25
Glen. 29d = 1
D. Maria. d= 10г +25
Glen: d = 291

Answer 1

To represent the situation mathematically, we can create a system of equations based on the distances biked by Maria and Glen over time.

1. Maria's equation: Maria starts at mile 10 and bikes at a speed of 25 km/h. The distance (d) biked by Maria after t hours can be expressed as: \[ d = 25t + 10 \]

2. Glen's equation: Glen starts at mile 0 and bikes at a speed of 29 km/h. The distance (d) biked by Glen after t hours can be expressed as: \[ d = 29t \]

Now, let's match these equations with the given options:

A. Maria: \(d = 25t + 10\)
Glen: \(d = 29t\)

B. Glen: \(d = 25t + 10\)
Maria: \(d = 29t\)

C. Maria: \(d = 10t + 25\)
Glen: \(29d = 1\)

D. Maria: \(d = 10t + 25\)
Glen: \(d = 29t\)

The correct representation matches the first option: A. Maria: d = 25t + 10; Glen: d = 29t.

So the answer is A.