I need help with some questions.

Question

Devin and Antonio are 192 miles apart, traveling towards each other. If Antonio travels 14 mph and Devin travels 10 mph how long until they meet?

Answer 1

In questions of this type, ask yourself which variable for each person is the same. If they both start out toward each other at the same time, when they meet they will have travelled the same time.

Using the formula distance = speed x time, solve for time for each person and set the expressions equal to each other.

time_devin = x / 10mph, time_ant, = 192-x / 14mph. Set these equal to each other and solve for x.

x / 10 = 192 -x / 14 to get x =80 miles. Substitute 80 in one of the time equations time_devin = 80 / 10 = 8 hours or time_ant = 192 - 80 /14 = 8 hours.

Answer 2

Hi Bon,

This is a classic distance (d) = rate (r) * time (t) problem. The question asks you what time Devin and Antonio will meet, so clearly, you need to solve for a time (t). Although there is not a ton of information, I suggest you write everything down. It is a good habit to develop for when you take more math courses in the future. So, what do you know?

Well, firstly, you know that the distance d = 192 mi. You also have two rates Antonio's rate (let's call it Ar) = 14 mph and Devin's rate (Dr) = 10 mph.

However, Devin and Antonio are going in opposite directions. If I had the option to draw, I would show you a line with a middle point showing where arrows pointing to each other meet. Anyway, you need to create a small system of equations using this meeting position, which we will call x.

So, the first equation is 192 - (Ar)*t = x and the second equation is (Dr)(t) = x. Because it is the same position, you can simply use the substitution method to create one easy equation in which you can solve for t. This equation becomes 192 -(Ar)t = (Dr)t. Now, let's plug the rates and distances we wrote down earlier and solve for t. So, you get 192 mph - (14 mph)*t =10 mph (t). Now, can you proceed and solve this single variable equation for t? If not, feel free to follow up with me.