Question

Two students are 1 foot apart on a straight path. each student starts walking away from the other at the same moment. the first student walks at a rate 3 feet per second, and the second students rate is 1.5 times the first students rate. if x represents seconds, which equation can be used to determine how long it will take for the students to be a totla of 28 feet apart?

a: 3 x + 1.5 x = 28
b: 3 x + 1.5 x + 1 = 28
c: 3 x + 4.5 x = 28
d: 3x+4.5x+1=28​

Answer 1

The correct equation to determine how long it will take for the two students to be 28 feet apart when they walk away from each other at rates of 3 feet per second and 4.5 feet per second is 3x + 4.5x = 28, which corresponds to choice (c).

Step-by-step explanation:

The question asks for the equation to determine how long it will take for the two students to be 28 feet apart if they start 1 foot apart and walk away from each other, with the first student walking at 3 feet per second and the second at 1.5 times that rate. Since distance is equal to speed multiplied by time, we use the rates provided to set up our equation. The second student's rate is 1.5 times the first student's rate, or 1.5 × 3 feet per second, which equals 4.5 feet per second.

Since both students are moving away from each other, we add their distances together to find the total distance apart. At any given second x, the first student covers 3x feet, and the second student covers 4.5x feet, resulting in a combined distance of 3x + 4.5x feet. They started 1 foot apart, but since they are moving in opposite directions, this initial distance does not need to be included in the equation, leading to the correct equation being 3x + 4.5x = 28. Therefore, the correct choice is (c).