Im completely confused with the answer...I know I must be overlooking something.
Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z ?
A 81
B 90
C 105
D 125
E 150
[spoiler]
E 150
If the answer is E, wouldn't car Y have traveled 135 miles further than car X?[/spoiler]
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Car X left Town T (RATE PROBLEM, Need Help)
This topic has expert replies
distance = speed x time
Car X travels at 40 mph for (z+18)mins = (z+18)/60 hours
Distance = 40(z+18)/60
Car Y travels at 54mph for z mins = z/60 hours
Distance = 54z/60
Car Y travels 23 miles more than Car X so:
(40(z+18)/60) + 23= 54z/60
40(z+18) + 23*60 = 54z (multiply through by 60)
40z + 720 + 1380 = 54z (multiplying out)
14z = 2100 (collecting like terms)
z = 150 (E)
Car X travels at 40 mph for (z+18)mins = (z+18)/60 hours
Distance = 40(z+18)/60
Car Y travels at 54mph for z mins = z/60 hours
Distance = 54z/60
Car Y travels 23 miles more than Car X so:
(40(z+18)/60) + 23= 54z/60
40(z+18) + 23*60 = 54z (multiply through by 60)
40z + 720 + 1380 = 54z (multiplying out)
14z = 2100 (collecting like terms)
z = 150 (E)
GMAT/MBA Expert
-
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
IMPORTANT: Let's use HOURS throughout our solution, and then convert hours to minutes at the end.mkbigmoz wrote:Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z ?
A 81
B 90
C 105
D 125
E 150
When car Y had traveled for z HOURS, car Y had traveled 23 miles more that car X had from the time that car X left Town T.
z = car Y's travel time in HOURS
So, z + 3/10 = car X's travel time in HOURS
[18 minutes = 3/10 HOURS, and car X traveled for 18 minutes before car Y started moving]
We can write: (car Y's distance traveled) - (car X's distance traveled) = 23 miles
distance = (speed)(time)
So, we get: (54)(z) - (40)(z + 3/10) = 23 miles
Expand to get: 54z - 40z - 12 = 23
Simplify: 14z - 12 = 23
So: 14z = 35
Solve: z = 35/14 = 5/2 = 2.5 HOURS
= 150 MINUTES
Answer: E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Let's make this into a simple D=RT problem. Since car X had been traveling for 18 minutes before car Y left, car X must be (18/60)hr*40mph = 12 miles ahead. Later, we learn that car Y had traveled 23 miles more than X. To sum it up, Car Y needs to catch up 35 miles to be 23 ahead of X.mkbigmoz wrote:Im completely confused with the answer...I know I must be overlooking something.
Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z ?
A 81
B 90
C 105
D 125
E 150
[spoiler]
E 150
If the answer is E, wouldn't car Y have traveled 135 miles further than car X?[/spoiler]
Car Y travels 14mph faster than Car X. So 35=14mph * t. 35/14 = 2.5 hrs = t. 2.5 hrs in minutes is 150.
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7245
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We are given that Car X traveled at a rate of 40 mph and Car Y at a rate of 54 mph.mkbigmoz wrote:Im completely confused with the answer...I know I must be overlooking something.
Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z ?
A 81
B 90
C 105
D 125
E 150
Since car Y left 18 minutes after car X, car Y traveled for z minutes, or z/60 hours, and car X for (z + 18) minutes or (z + 18)/60 hours; thus:
40[(z + 18)/60] + 23 = 54(z/60)
Multiplying by 60, we have:
40(z + 18) + 1380 = 54z
40z + 720 + 1380 = 54z
2100 = 14z
z = 2100/14 = 150
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
