Official Guide
A driver completed the first 20 miles of a 40 miles trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-miles trip? (Assume that the driver did not make any stops during the 40-miles trip)
A. 65
B. 68
C. 70
D. 75
E. 80
OA D
A driver completed the first 20 miles of a 40 miles trip at
This topic has expert replies
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Say the average speed the driver clocks for the remaining 20 miles to achieve an average speed of 60 miles per hour = x miles per hourAAPL wrote:Official Guide
A driver completed the first 20 miles of a 40 miles trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-miles trip? (Assume that the driver did not make any stops during the 40-miles trip)
A. 65
B. 68
C. 70
D. 75
E. 80
OA D
The average speed of the 40 miles = Total distance / Total time = 40 / (20/50 + 20/x)
60 = 40 / (20/50 + 20/x)
20/50 + 20/x = 40/60
2/5 + 20/x = 2/3
20/x = 2/3 - 2/5
x/20 = 4/16
x = 75 mph
The correct answer: D
Hope this helps!
-Jay
_________________
Manhattan Review
Locations: Manhattan Review Kukatpally | GMAT Prep Jayanagar | GRE Prep Tarnaka | Madhapur GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
We can use the following formula:AAPL wrote:Official Guide
A driver completed the first 20 miles of a 40 miles trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-miles trip? (Assume that the driver did not make any stops during the 40-miles trip)
A. 65
B. 68
C. 70
D. 75
E. 80
average rate = (distance 1 + distance 2)/(time 1 + time 2)
where average rate = 60, distance 1 = distance 2 = 20, time 1 = distance 1/rate 1 = 20/50 = 2/5, and time 2 = distance 2/rate 2 = 20/r (where r is the average speed of the remaining 20 miles).
Let's now determine r:
60 = (20 + 20)/(2/5 + 20/r)
60 = 40/(2r/5r + 100/5r)
60 = 40/[(2r + 100)/5r]
60 = 200r/(2r + 100)
60(2r + 100) = 200r
120r + 6000 = 200r
6000 = 80r
r = 6000/80 = 600/8 = 75
Alternate Solution:
In order to achieve an average speed of 60 mph, the driver must complete the entire journey in 40/60 = 2/3 hours. Note that he already spent 20/50 = 2/5 hours on the first 20 miles of the trip; thus he must complete the remaining 20 miles in 2/3 - 2/5 = 4/15 hours. To travel 20 miles in 4/15 hours, his rate must be 20/(4/15) = (20 * 15)/4 = 5 * 15 = 75 mph.
Answer: D
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews