Question 251841: A and B, traveling at respective rates of a and b kilometers per hour, head directly towards each other across a distance of 120 kilometers. If both start at 10:30 a.m., they will meet at noon. If A starts at 10:00 a.m. and B starts at 11:00 a.m., they will also meet at noon. Find the ordered pair (a,b).
a) (30,30) b) (30,40) c) (40,40) d) (40,30) e) none of these
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A and B, traveling at respective rates of a and b kilometers per hour, head directly towards each other across a distance of 120 kilometers. If both start at 10:30 a.m., they will meet at noon. If A starts at 10:00 a.m. and B starts at 11:00 a.m., they will also meet at noon. Find the ordered pair (a,b).
:
When a meets b, their total travel dist = 120 km;
:
Travel time of both starting at 1:30: 1.5 hrs
When a starts at 10: 2 hrs
When b starts at 11: 1 hr
:
Write two distance equations; Dist = speed * time
1.5a + 1.5b = 120
and
2a + 1b = 120
or
b = 120-2a
:
Substitute above for b in the 1st equation, find a
1.5a + 1.5(120-2a) = 120
1.5a + 180 - 3a = 120
1.5a - 3a = 120 - 180
-1.5a = -60
a = 
a = 40
and
b = 120 - 2(40)
b = 120 - 80
b = 40
:
Ordered pair, 40,40
:
:
Check solution in 2nd equation
2(40) + 1(40) = 120
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