SOLUTION: Carl can walk from his home to school in 30 minutes. It takes his sister 35 minutes to walk the same distance. How long would it take them to meet, if one started from school and

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Question 408171: Carl can walk from his home to school in 30 minutes. It takes his sister 35 minutes to walk the same distance. How long would it take them to meet, if one started from school and the other at home at the same time and they walked toward each other at their usual speeds.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Carl can walk from his home to school in 30 minutes.
It takes his sister 35 minutes to walk the same distance.
How long would it take them to meet, if one started from school and the other
at home at the same time and they walked toward each other at their usual speeds
:
let t = time to meet walking towards each other
:
Let d = the distance from home to school
then
d%2F30 = C's walking speed
and
d%2F35 = S's walking speed
:
Write a distance equation; dist = speed * time
:
C's dist + S's dist = total dist
t(d%2F30) + t(d%2F35) = d
:
divide thru by d, we don't need that, results:
(t%2F30) + (t%2F35) = 1
multiply by 210 to clear the denominators
7t + 6t = 210
13t = 210
t = 210%2F13
t = 16.154 minutes for them to meet
:
:
prove our solution with some real numbers, let d = 210 units
then
210/30 = 7 units per minute is C's walking speed
and
210/35 = 6 units per minute is S's walking speed
:
Find the total distance they walked in 16.154 min
16.154(7) = 16.154(6) =
113.078 + 96.924 = 210.00 confirms our solution of t = 16.154 minutes