Answer:
It seems like the chat transitioned to a different topic. However, based on the search results, it appears that the query was related to solving distance problems using linear equations. One common application of linear equations is in distance problems, where you can create and solve linear equations to find the distance between two points or the rate of travel. Here's an example problem:
Joe drove from city A to city B, which are 120 miles apart. He drove part of the distance at 60 miles per hour (mph) and the rest at 40 mph. If the entire trip took three hours, how many miles did he drive at each speed?
To solve this problem, you can use a system of two linear equations. Let x be the number of miles driven at 60 mph, and y be the number of miles driven at 40 mph. Then you have:
x + y = 120 (total distance is 120 miles) x/60 + y/40 = 3 (total time is 3 hours)
To solve for x and y, you can multiply the second equation by 120 to eliminate fractions and then use the first equation to solve for one of the variables. For example:
x/60 + 3y/120 = 3 x/60 + y/40 = 3 2x/120 + 3y/120 = 3 x/60 + y/40 = 3 x/60 = 3 - y/40 x = 180 - 3y/2 (from the first equation)
Substitute the expression for x into the second equation and solve for y:
x/60 + y/40 = 3 (180 - 3y/2)/60 + y/40 = 3 3 - 3y/160 + y/40 = 3 3 - 3y/160 = 2.75 -3y/160 = -0.25 y = 20
Substitute y = 20 into the expression for x to get:
x = 180 - 3y/2 x = 120
Therefore, Joe drove 120 - 20 = 100 miles at 60 mph and 20 miles at 40 mph.
Explanation: