A man (we'll refer to him as man 1) starts from his home at 8 A.M. and drives a steady rate of 50 MPH. An hour later a second man ( man 2) starts to follow him. Draw a graph to represent these facts. From the graph find when man 2 overtakes man 1. Okay, I imagined at 9 A.M. man 1 has reached the 50 mile marker, and man two is "following" him. We don't know how far along he is or what time he departed. The distance he is behind him is X= x-50
and at 10 A.M. He will be 55+ x ahead. Please help me. My brain feels foggy.
There is no unique solution to your problem.
Let the time spent driving by man1 be 1 hours
then the time for man2 when he overtook man1 is t-1 hours.
let the speed of man2 be x mph
distance driven by man1 = 50t miles
distance driven by man2 = x(t-1) miles
but at the overtake, the both went the same distance, so
x(t-1) = 50t
xt - x = 50t
xt-50t = x
t(x-50) = x
t = x/(x-5) , clearly x > 50
let x = 60, then
t = 60/10 = 6 hours
check: when t = 6 hours,
distance of man 1 = 300 miles
time for second man = 5 hours, speed of second man = 60 mph, distance = 300
try x=70 , so t = 3.5
distance of man1 = 3.5x50 = 175 miles
time for second man = 2.5, speed of second man = 70
distance of second man = 2.5x70 = 175
notice both combination of answers work, as will as many others as you want.
We know man 1 drives 50 miles per hour
man 2 goes 55 mph
The answer differs from yours.
Please help! I'm still waiting!
To represent the situation on a graph, we can use the x-axis to represent time (in hours) and the y-axis to represent distance (in miles).
Since man 1 starts at 8 A.M. and drives at a steady rate of 50 MPH, his position can be represented by a line with a slope of 50/1 (50 miles per hour) starting from point (0, 0).
Since man 2 starts an hour later, his position will always be behind man 1. Let's assume that at 9 A.M., man 1 has reached the 50-mile marker, and man 2 is following him. To find when man 2 overtakes man 1, we need to find the point where man 2's position line intersects/man 1's position line.
We can express man 1's position line as y = 50x, where x represents the time in hours. Since man 2 starts an hour later and drives at the same rate, his position line can be expressed as y = 50(x-1).
To find the point of intersection, we equate the two equations and solve for x:
50x = 50(x-1)
50x = 50x - 50
50x - 50x = -50
0 = -50
There is no solution to this equation, which means that man 2 never overtakes man 1. In other words, man 1 will always be ahead of man 2.
So, based on the given information, man 2 will not overtake man 1.