SOLUTION: Hillary and Charlene both drove from City A to City B. At 10a, Hilary left City A and drove at an average speed of 120km/h. Charlene drove at an average speed of 144 km/h and took

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Hillary and Charlene both drove from City A to City B. At 10a, Hilary left City A and drove at an average speed of 120km/h. Charlene drove at an average speed of 144 km/h and took       Log On

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Question 1150545: Hillary and Charlene both drove from City A to City B. At 10a, Hilary left City A and drove at an average speed of 120km/h. Charlene drove at an average speed of 144 km/h and took 50 mins. She arrived at City B at the same time as Hillary. Find the time Charlene left City A.
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d%5B1%5D+ = Hillary's head start in km
Let +d+ = the distance between city A and city B
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Start a stop watch when Charlene leaves city A
Hillary's equation:
(1) +d+-+d%5B1%5D+=+120%2A%28+50%2F60+%29+
Charlene's equation:
(2) +d+=+144%2A%28+50%2F60+%29+
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By substitution:
(1) +144%2A%28+50%2F60+%29+-+d%5B1%5D+=+120%2A%28+50%2F60+%29+
Multiply both sides by +60%2F50+
(1) +144+-+%28+60%2F50+%29%2Ad%5B1%5D+=+120+
(1) +%28+6%2F5+%29%2Ad%5B1%5D+=+24+
(1) +d%5B1%5D+=+%28+5%2F6+%29%2A24+
(1) +d%5B1%5D+=+20+ km
Plug this result back into (1)
(1) +d+-+d%5B1%5D+=+120%2A%28+50%2F60+%29+
(1) +d+-+20+=+120%2A%28+50%2F60+%29+
(1) +d+=+100+%2B+20+
(1) +d+=+120+
---------------------------
Charlene took 50 minutes after the time that
Hillary drove +d%5B1%5D+ km
+20+=+120%2At+
+t+=+10%2F60+
Charlene left city A at 10:10 AM
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check:
(1) +d+-+d%5B1%5D+=+120%2A%28+50%2F60+%29+
(1) +120+-+20+=+120%2A%28+50%2F60+%29+
(1) +100+=+100+
and
(2) +d+=+144%2A%28+50%2F60+%29+
(2) +120+=+144%2A%28+50%2F60+%29+
(2) +120+=+120+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The distances are the same; the speeds are in the ratio 120:144 = 5:6. That means the times are in the ratio 6:5.

Charlene took 50 minutes at the higher speed, so Hillary took 60 minutes.

So Charlene took 10 minutes less than Hillary; since Hillary left at 10am, and since they arrived at the same time, Charlene left at 10:10am.