SOLUTION: bobby left the space museum and drove south nancy left three hours later driving 42 km/h faster in an effort to catch up to him after two hours nancy finally caught up find bobby's

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Question 1109901: bobby left the space museum and drove south nancy left three hours later driving 42 km/h faster in an effort to catch up to him after two hours nancy finally caught up find bobby's average speed
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Bobby's average speed
Bobby's head start is:
+d%5B1%5D+=+s%2A3+ km
----------------
Nancy's average speed is:
+s+%2B+42+ km
-------------------------
Let +d+ = The distance Nancy traveled
until she caught up with Bobby
----------------------------------
Nancy's equation:
(1) +d+=+%28+s+%2B+42+%29%2A2+
Bobby's equation:
(2) +d+-+3s+=+s%2A2+
----------------------------
Plug (1) into (2)
(2) +%28+s+%2B+42+%29%2A2+-+3s+=+2s+
(2) +2s+%2B+84+-3s+=+2s+
(2) +3s+=+84+
(2) +s+=+28+ km/hr
-----------------------------
Bobby's average speed is 28 km/hr
---------------------------------
check answer:
(1) +d+=+%28+28+%2B+42+%29%2A2+
(1) +d+=+140+ km
and
(2) +d+-+3%2A28+=+2%2A28+
(2) +d+-+84+=+56+
(2) +d+=+140+ km
OK

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Nancy had to drive only 2 hours to catch up to Bobby, who drove for 5 hours. Since the distances were the same and the ratio of times was 2:5, the ratio of speeds was 5:2.

Let Bobby's speed by 2x and Nancy's speed be 5x. Nancy's speed is 42km/h faster than Bobby's:
5x-2x=42
3x=42
x+=+14

Bobby's speed was 2x = 28km/hr; Nancy's was 5x = 70km/hr.