SOLUTION: Kayla can run 100 yards in 12 seconds. Naomi can run the same distance in 16 seconds. If Naomi is 20 yards ahead of Kayla when they both start running, how long does it take for Ka

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Kayla can run 100 yards in 12 seconds. Naomi can run the same distance in 16 seconds. If Naomi is 20 yards ahead of Kayla when they both start running, how long does it take for Ka      Log On

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Question 1097199: Kayla can run 100 yards in 12 seconds. Naomi can run the same distance in 16 seconds. If Naomi is 20 yards ahead of Kayla when they both start running, how long does it take for Kayla to catch Naomi?
A) How long does it take for Kayla to catch Naomi? (in seconds)
B How many yards does Kayla have to run to catch Naomi?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Kayla's speed = +100%2F12+=+25%2F3+ yds/sec
Naomi's speed = +100%2F16+=+25%2F4+ yds/sec
Let +d+ = distance that Kayla runs
until she catches Naomi
Let +t+ = time in seconds until
Kayla catch up with Naomi
--------------------------------------
Start a stop watch at +t=0+
when Kayla leaves
Naomi's head start is +20+ yds
--------------------------------------
Kayla's equation:
(1) +d+=+%28+25%2F3+%29%2At++
Naomi's equation:
(2) +d+-+20+=+%28+25%2F4+%29%2At+
----------------------------
Plug (1) into (2)
+%2825%2F3%29%2At+-+20+=+%28+25%2F4+%29%2At+
Multiply both sides by +12+
+100t+-+240+=+75t+
+25t+=+240+
+t+=+240%2F25+
+t+=+9.6+ sec
Kayla catches Naomi in 9.6 sec
------------------------------
check:
(1) +d+=+%2825%2F3%29%2At+
(1) +d+=+%2825%2F3%29%2A9.6+
(1) +d+=+8.333%2A9.6+
(1) +d+=+80+ yds
and
(2) +d+-+20+=+%28+25%2F4+%29%2At+
(2) +d+-+20+=+6.25%2A9.6+
(2) +d+-+20+=+60+
(2) +d+=+80+ yds
OK