Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?
A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00
The OA is C.
I get the solution in the following way,
Car A: 65m/h
Car B: 50m/h
Houston to morse = m = distance
speed=disttimespeed=disttime
Car A:
65m/h=mt
m=65*t ....equation 1
Car B:
50m/h=2m(t+2)
2m=50*t+50∗2
m=25*t+50....equation 2
Combining equation 1 and 2
65*t=25*t+50
40*t=50
t=5/4
t=1,25.
Please, can anyone explain another way to get the solution? Thanks!
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Both car A and car B set out from their original locations..
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BTGmoderatorLU
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All's fine except a couple of typos. I highlighted them in red.BTGmoderatorLU wrote:Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?
A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00
The OA is C.
I get the solution in the following way,
Car A: 65m/h
Car B: 50m/h
Houston to morse = m = distance
speed=disttimespeed=disttime
Car A:
65m/h=m / t
m=65*t ....equation 1
Car B:
50m/h=2m / (t+2)
2m=50*t+50∗2
m=25*t+50....equation 2
Combining equation 1 and 2
65*t=25*t+50
40*t=50
t=5/4
t=1,25.
Please, can anyone explain another way to get the solution? Thanks!
-Jay
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GMATGuruNY
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Let t = A' s time, implying that t+2 = B's time.BTGmoderatorLU wrote:Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?
A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00
Since A's rate = 65 mph, the total distance traveled by A in t hours = 65t.
Since B's rate = 50 mph, the total distance traveled by B in t+2 hours = 50(t+2).
Since B travels BACK AND FORTH, while A travels only in only ONE DIRECTION, B's total distance must be twice A's total distance:
50(t+2) = 2(65t)
50t + 100 = 130t
100 = 80t
t = 100/80 = 5/4 = 1.25.
The correct answer is C.
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Scott@TargetTestPrep
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We can let the distance between Morse and Houston = d miles. So the time it takes car A to drive from Morse to Houston is d/65. Since car B arrives in Houston 2 hours after car A and it also drives double the distance, we can create the following equation:BTGmoderatorLU wrote:Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?
A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00
2d/50 = d/65 + 2
Multiplying both sides by 650, we have:
26d = 10d + 1300
16d = 1300
d = 81.25
Therefore, it takes car A 81.25/65 = 1.25 hours to make the trip from Morse to Houston.
Alternate Solution:
Let the time car A takes to drive from Morse to Houston be t. Since car A drives at 65 mph, the distance between Morse and Houston, in terms of t, is 65t.
We are given that it takes t + 2 hours for car B to drive twice the distance between Morse and Houston; thus:
65t = [50(t + 2)]/2
130t = 50t + 100
80t = 100
t = 100/80 = 5/4 = 1.25 hours
Answer: C
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