SOLUTION: Please help me in my assignment I'm sorry to say that I'm very poor in worded problems. This is a take home quiz and i dn't know where our teacher get it. so here is my question..

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Question 151349: Please help me in my assignment I'm sorry to say that I'm very poor in worded problems. This is a take home quiz and i dn't know where our teacher get it.
so here is my question......
2 boys are 96yards apart.if they run towards each other they will meet in 8secs.
if they run at the same starting point the faster boy overtake the slower boy in 48 seconds.Find the rate of each.
I don't know if my answer is correct. Please send me the step by step solution so that i can study it. Thank you
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
2 boys are 96yards apart.if they run towards each other they will meet in 8secs.
if they run at the same starting point the faster boy overtake the slower boy in 48 seconds.Find the rate of each.:
:
Solve this using two equations:
:
let x = rate of the 1st boy (in yd/sec}
let y = rate of the 2nd boy
:
Write a distance equation from the 1st statement: Dist = time * rate
8x + 8y = 96
:
Using the 2nd statement,
we know that when one overtakes the other, one will have to go 96 yds further.
Fast boy dist = slow boy dist + 96
48x = 48y + 96
48x - 48y = 96
:
Multiply the 1st equation by 6 and add to the 2nd equation:
48x + 48y = 576
48x - 48y = 96
----------------addition eliminates y
96x = 672
x =
x = 7 yd/sec
;
Find y:
8(7) + 8y = 96
56 + 8y = 96
8y = 96 - 56
y =
y = 5 yd/sec
:
Check solution using the 2nd equation
48(7) = 48(5) + 96
336 = 240 + 96