On a 20 mile course, Pat bicycled at an average rate of 30

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AAPL: Moderator; Posts: 2710; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Tue Oct 02, 2018 3:06 am

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On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?

A. 75
B. 105
C. 117
D. 150
E. 162

OA C.

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Source: Beat The GMAT — Problem Solving | Tue Oct 02, 2018 3:06 am

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by GMATGuruNY » Tue Oct 02, 2018 3:22 am

AAPL wrote:GMAT Paper Tests

On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?

A. 75
B. 105
C. 117
D. 150
E. 162

Since Pat travels at 30 miles per hour for the first 12 minutes -- the equivalent of 1/5 hour -- the distance traveled in the first 12 minutes = (30)(1/5) = 6 miles.
Since the remaining 14 miles are traveled at 8 miles per hour, the time to travel the remaining 14 miles = 14/8 = 7/4 hours = 1 hour + 3/4 hour = 60 minutes + 45 minutes = 105 minutes.
Total time for the entire 20-mile trip = 12 + 105 = 117 minutes.

The correct answer is C.

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by Brent@GMATPrepNow » Tue Oct 02, 2018 6:12 am

AAPL wrote:GMAT Paper Tests

On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?

A. 75
B. 105
C. 117
D. 150
E. 162

OA C.

Let's start with a WORD EQUATION

(Distance traveled at 30 mph) + (Distance traveled at 8 mph) = 20 miles

Distance = (rate)(time)
Let t = the time (in hours) Pat spent running at 8 mph
Aside: 12 minutes = 1/5 hours

So, we get: (30 miles per hour)(1/5 hours) + (8 miles per hour)(t hours) = 20 miles
Simplify: 6 + 8t = 20
So: 8t = 14
t = 14/8 = 7/4 = 1.75 hours = 105 minutes

How many minutes did Pat take to cover the entire course?
Pat spent 12 minutes riding a bike, and 105 minutes running
TOTAL time = 12 + 105 = 117

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8211; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Oct 03, 2018 4:58 pm

AAPL wrote:GMAT Paper Tests

On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?

A. 75
B. 105
C. 117
D. 150
E. 162

Pat biked 30 x 12/60 = 6 miles.

Thus, he ran 14 miles. This took him 14/8 = 7/4 = 1 3/4 = 1 hour and 45 minutes = 105 minutes.

So, in total, Pat took 12 + 105 = 117 minutes to complete the course.

Answer: C

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