SOLUTION: 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
Algebra.Com
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
RELATED QUESTIONS
A and B, traveling at respective rates of a and b kilometers per hour, head directly... (answered by richwmiller)
A and B, traveling at respective rates of a and b kilometers per hour, head directly... (answered by checkley77)
Car A and Car B are 456 miles apart and are travelling towards each other at the rates of (answered by josmiceli)
Two buses are traveling towards each other and are doing dead-runs. One bus left the... (answered by JulietG)
Ashlee and Jennifer are coworkers who live in different cities. They both left the office (answered by richwmiller)
Two cyclist start 10 kilometers apart. They are traveling towards each other, cyclist A... (answered by nerdybill)
The distance between two stations A and B is 240km. Two trains leaved both stations at... (answered by mananth)
Two trains traveling on parallel tracks are going toward each other from a distance of... (answered by Edwin McCravy)
Two skiers are 62.5 kilometers apart and head towards each other. They meet in 2.5 hours. (answered by JulietG)