Posted by **Amal** on Tuesday, June 8, 2010 at 4:08pm.

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.

- algebra -
**Reiny**, Tuesday, June 8, 2010 at 5:11pm
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 -
**Amal**, Tuesday, June 8, 2010 at 5:49pm
We know man 1 drives 50 miles per hour

man 2 goes 55 mph

- algebra -
**Amal**, Wednesday, June 9, 2010 at 11:32am
The answer differs from yours.

- algebra -
**Amal**, Tuesday, June 15, 2010 at 6:08pm
Please help! I'm still waiting!

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