Bill spends two days driving from Point A to Point B. On the first

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

Bill spends two days driving from Point A to Point B. On the first

by BTGModeratorVI » Sun Aug 02, 2020 6:58 am

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Bill spends two days driving from Point A to Point B. On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?

A) 20
B) 25
C) 28
D) 30
E) 35

Answer: E
Source: Kaplan

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Source: Beat The GMAT — Problem Solving | Sun Aug 02, 2020 6:58 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

Re: Bill spends two days driving from Point A to Point B. On the first

by Brent@GMATPrepNow » Wed Aug 05, 2020 6:19 am

BTGModeratorVI wrote: ↑
Sun Aug 02, 2020 6:58 am
Bill spends two days driving from Point A to Point B. On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?

A) 20
B) 25
C) 28
D) 30
E) 35

Answer: E
Source: Kaplan

First recognize that we have TWO pieces of information regarding the time Bill spent driving each day.
On day 1, Bill drove 2 hours longer than he drove on day 2.
So, let x = # of driving hours on day 2
Then x + 2 = # of driving hours on day 1

Bill drove a TOTAL of 18 hours
So, x + (x + 2) = 18
Simplify: 2x + 2 = 18
Solve, x = 8
So, Bill drove 10 hours on day 1 and he drove 8 hours on day 2

Now let's solve the question by starting with a word equation.
Let x = speed driven on day 2
So, x + 5 = speed driven on day 1

(Distance traveled on day 1) + (Distance traveled on day 2) = 680
Distance = (rate)(time)
We get: (x+ 5)(10) + (x)(8) = 680
Expand: 10x + 50 + 8x = 680
Simplify: 18x + 50 = 680
18x = 630
x = 35 (mph)

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8084; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Bill spends two days driving from Point A to Point B. On the first

by Scott@TargetTestPrep » Mon Aug 10, 2020 3:18 am

BTGModeratorVI wrote: ↑
Sun Aug 02, 2020 6:58 am
Bill spends two days driving from Point A to Point B. On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?

A) 20
B) 25
C) 28
D) 30
E) 35

Answer: E

Solution:

We are given that on the first day, Bill drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. We can let the rate on the second day = r and the rate on the first day = r + 5. Also, we can let the time on the second day = t and the time on the first day = t + 2.

Since the total time is 18, we can create the following equation to determine t:

t + t + 2 = 18

2t = 16

t = 8

Thus, the distance on day 2 is 8r and the distance on day 1 is (r + 5)(10) = 10r + 50

We can create the following equation to determine r:

8r + 10r + 50 = 680

18r = 630

r = 35

Answer: E

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