Car X and Car Y traveled the same 80-mile route...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Car X and Car Y traveled the same 80-mile route...

by swerve » Sun Jan 28, 2018 6:44 am

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Car X and Car Y traveled the same 80-mile route. If Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X, how many hours did it take Car Y to travel the route?

A. 2/3
B. 1
C. 4/3
D. 8/5
E. 3

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Jan 28, 2018 6:44 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Jan 28, 2018 7:45 am

swerve wrote:Car X and Car Y traveled the same 80-mile route. If Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X, how many hours did it take Car Y to travel the route?

A. 2/3
B. 1
C. 4/3
D. 8/5
E. 3

There's a nice rule we can use here.

To set up the rule, recognize that if Y travels 2 times as fast as X, then Y's travel time will be 1/2 of X's.
Similarly, if Y travels 3 times as fast as X, then Y's travel time will be 1/3 of X's.
Or if Y travels 1/4 as fast as X, then Y's travel time will be 4 times X's travel time.

In general, if Y travels a/b times as fast as X, then Y's travel time will be b/a of X's travel time.

So, if Y's speed is 50% more than X's speed, we can say that Y travels 1.5 times as fast as X.
In other words, if Y travels 3/2 times as fast as X, which means Y's travel time will be 2/3 that of X's travel time.

Since X's travel time is 2 hours, Y's travel time will be (2/3)(2) = 4/3 = 1 1/3 = C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sun Jan 28, 2018 12:33 pm

Hi swerve,

We're told that Car X and Car Y traveled the same 80-mile route, Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X. We're asked for the number of hours it took Car Y to travel the route. With a few standard 'math steps', you can answer this question without too much difficulty.

To start, we can calculate Car X's speed using the Distance Formula:
Distance = (Rate)(Time)
80 miles = (Rate)(2 hours)
80/2 = Rate
Rate = 40 miles/hour

Since Car Y's speed was 50% GREATER than Car X's speed, we can now calculate that speed:
(1.5)(40 miles/hour) = 60 miles/hour

Using that speed, we can calculate how long it took Car Y to travel that same distance:
Distance = (Rate)(Time)
80 miles = (60 miles/hour)(Time)
80/60 = Time
Time = 80/60 = 8/6 = 4/3 hours

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jul 12, 2019 6:00 pm

swerve wrote:Car X and Car Y traveled the same 80-mile route. If Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X, how many hours did it take Car Y to travel the route?

A. 2/3
B. 1
C. 4/3
D. 8/5
E. 3

We are given that Car X traveled 80 miles in 2 hours. Thus, the rate of Car X was 80/2 = 40 mph.

We are also given that Car Y traveled 50% faster than Car X. Thus, Car Y traveled at a rate of 1.5 x 40 = 60 mph.

So, it took Car Y 80/60 = 8/6 = 4/3 hours to travel the same route.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]