# algebra

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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

• algebra -

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.

• algebra -

We know man 1 drives 50 miles per hour
man 2 goes 55 mph

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• algebra -