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Car X is 40 miles west of Car Y. Both cars are travelling ea
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10 Jun 2020, 22:05
10 Jun 2020, 22:05
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Car X is 40 miles west of Car Y. Both cars are travelling east and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hrs 40 min to catch up to Car Y, how fast is Car Y going?
A) 20 m/h
B) 25 m/h
C) 30 m/h
D) 35 m/h
E) 40 m/h
A) 20 m/h
B) 25 m/h
C) 30 m/h
D) 35 m/h
E) 40 m/h
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Car X is 40 miles west of Car Y. Both cars are travelling ea
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11 Jun 2020, 02:19
11 Jun 2020, 02:19
3
Let's let Car X's original position be the initial starting point.
So, when Car X is at the initial starting point, Car Y has already traveled 40 miles.
My word equation involves the conditions when Car X catches up to Car Y.
At that point, we can say:
Car X's TOTAL distance traveled = Car Y's TOTAL distance traveled
Car Y's total distance
Let V = Car Y's speed (our goal is to find the value of V)
From the time that Car X begins moving, Car Y drives for 2 2/3 hours (2 hours, 40 minutes).
So Car Y's total distance = (time)(speed) = (2 2/3)(V) + 40 miles
Car X's total distance
We know that Car X is going 50% faster than Car Y. If Car Y's rate is V, then Car X's rate must be 1.5V
We also know that Car X travels for 2 2/3 hours.
So Car X's total distance = (time)(speed) = (2 2/3)(1.5V) miles
Simplify: (2 2/3)(1.5V) = (8/3)(3/2) = 4V
We're now ready to write our algebraic equation.
Car X's total distance = Car Y's total distance
4V = (2 2/3)(V) + 40 miles
4/3V = 40
V = 40(3/4)
V = 30
Cheers,
Brent
So, when Car X is at the initial starting point, Car Y has already traveled 40 miles.
My word equation involves the conditions when Car X catches up to Car Y.
At that point, we can say:
Car X's TOTAL distance traveled = Car Y's TOTAL distance traveled
Car Y's total distance
Let V = Car Y's speed (our goal is to find the value of V)
From the time that Car X begins moving, Car Y drives for 2 2/3 hours (2 hours, 40 minutes).
So Car Y's total distance = (time)(speed) = (2 2/3)(V) + 40 miles
Car X's total distance
We know that Car X is going 50% faster than Car Y. If Car Y's rate is V, then Car X's rate must be 1.5V
We also know that Car X travels for 2 2/3 hours.
So Car X's total distance = (time)(speed) = (2 2/3)(1.5V) miles
Simplify: (2 2/3)(1.5V) = (8/3)(3/2) = 4V
We're now ready to write our algebraic equation.
Car X's total distance = Car Y's total distance
4V = (2 2/3)(V) + 40 miles
4/3V = 40
V = 40(3/4)
V = 30
Cheers,
Brent
Re: Car X is 40 miles west of Car Y. Both cars are travelling ea
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04 Jun 2022, 13:24
04 Jun 2022, 13:24
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
