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Alice and Bob drive the same car. Alice drives the car for 1

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by Max@Math Revolution » Mon Jun 25, 2018 3:01 am

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[GMAT math practice question]

Alice and Bob drive the same car. Alice drives the car for 1/4 of one trip, and Bob drives the car for the remainder of the same trip. The difference between the distance driven by Bob and the distance driven by Alice is 40 km. What is the total distance travelled on the trip?

A. 60 miles
B. 80 miles
C. 100 miles
D. 120 miles
E. 125 miles
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by GMATGuruNY » Mon Jun 25, 2018 5:01 am
The prompt should specify that 1/4 of the trip = 1/4 of the total distance.
Max@Math Revolution wrote:[GMAT math practice question]

Alice and Bob drive the same car. Alice drives the car for 1/4 of one trip, and Bob drives the car for the remainder of the same trip. The difference between the distance driven by Bob and the distance driven by Alice is 40 km. What is the total distance travelled on the trip?

A. 60 miles
B. 80 miles
C. 100 miles
D. 120 miles
E. 125 miles
We can PLUG IN THE ANSWERS, which represent the total distance.
When the correct answer is plugged in, the difference between Bob's distance and Alice's distance = 40 km.

B: 80 km
Alice's distance = (1/4)(80) = 20 km.
Bob's distance = (total distance) - (Alice's distance) = 80 - 20 = 60.
Difference between Bob's distance and Alice's distance = 60 - 20 = 40 km.
Success!

The correct answer is B.
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by Brent@GMATPrepNow » Mon Jun 25, 2018 6:29 am
Max@Math Revolution wrote:[GMAT math practice question]

Alice and Bob drive the same car. Alice drives the car for 1/4 of one trip, and Bob drives the car for the remainder of the same trip. The difference between the distance driven by Bob and the distance driven by Alice is 40 km. What is the total distance travelled on the trip?

A. 60 miles
B. 80 miles
C. 100 miles
D. 120 miles
E. 125 miles
Let T = total distance traveled

Alice drives the car for 1/4 of one trip, and Bob drives the car for the remainder of the same trip
In other words, Bob drove 3/4 the distance.
We can write: (1/4)T = distance Alice drove
And (3/4)T = distance Bob drove

The difference between the distance driven by Bob and the distance driven by Alice is 40 km.
We can write: (3/4)T - (1/4)T = 40
Multiply both sides by 4 to get: 3T - T = 160
Simplify: 2T = 160
Solve: T = 80

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by swerve » Tue Jun 26, 2018 9:18 am
Let distance driven by Bob be B and distance drove by Alice be A. Let the total distance be X.

B - A = 40 km

B = 3X/4 and A = X/4

B - A = 3X - X/4 = 2X/4 = X/2

X/2 = 40 km.

Therefore, X = 80 km. Hence, B is the correct answer.
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by Max@Math Revolution » Wed Jun 27, 2018 12:48 am
=>

Let d be the total distance traveled on the trip.
Alice drives (1/4)d and Bob drives (3/4)d.
The difference between the distances they drive is (3/4)d - (1/4)d = (1/2)d = 40.
Thus, d = 80.

Therefore, the answer is B.
Answer: B
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by Jeff@TargetTestPrep » Thu Jun 28, 2018 6:26 am
Max@Math Revolution wrote:[GMAT math practice question]

Alice and Bob drive the same car. Alice drives the car for 1/4 of one trip, and Bob drives the car for the remainder of the same trip. The difference between the distance driven by Bob and the distance driven by Alice is 40 km. What is the total distance travelled on the trip?

A. 60 miles
B. 80 miles
C. 100 miles
D. 120 miles
E. 125 miles
We can let x = the total distance of the trip in miles. Thus, Alice drove (1/4)x miles and Bod drove (3/4)x miles, and we have:

(3/4)x - (1/4)x = 40

(1/2)x = 40

x = 80

Answer: B

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