SOLUTION: At 3pm Mark left Pittsburg and drove towards Cleveland, 208 km away. At 3:30 pm Carole left Cleveland and headed towards Pittsburg, driving 2 km/h slower than MArk. If there cars p

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: At 3pm Mark left Pittsburg and drove towards Cleveland, 208 km away. At 3:30 pm Carole left Cleveland and headed towards Pittsburg, driving 2 km/h slower than MArk. If there cars p      Log On

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Question 1012481: At 3pm Mark left Pittsburg and drove towards Cleveland, 208 km away. At 3:30 pm Carole left Cleveland and headed towards Pittsburg, driving 2 km/h slower than MArk. If there cars passed each other at 4:30, how fast was each driving
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How much was Mark's head start?
Let +r+ = Marks rate in km/hr
Let +d+ = Mark's head start in km
+t+=+1%2F2+ hr
+d%5B1%5D+=+r%2At+
+d%5B1%5D+=+r%2A%281%2F2%29+
-----------------
Start a stopwatch when Carole leaves Cleveland
Let +d+ = distance Carole travels until they meet
+r+-+2+ = Carole's rate in km/hr
From 3:30 to 4:30 is +1+ hr, so
Carole's equation is:
+d+=+%28+r+-+2+%29%2A1+
-------------------
Mark's equation:
+208+-+r%2A%281%2F2%29+-+%28+r+-+2+%29%2A1+=+r%2A1+
+208+-+r%2F2+-+r+%2B+2+=+r+
+r+%2B+r+%2B+r%2F2+=+210+
+%285%2F2%29%2Ar+=+210+
+r+=+%282%2F5%29%2A210+
+r+=+84+ km/hr
and
+r+-+2+=+82+ km/hr
Mark's rate was 84 km/hr
Carole's rate was 82 km/hr
------------------------
check:
Carole's distance:
+d+=+%28+r+-+2+%29%2A1+
+d+=+82+ km
Mark must have traveled +208+-+82+=+126+ km
in +3%2F2+ hrs at +84+ km/hr
+126+=+84%2A%283%2F2%29+
+126+=+126+
OK