It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike retur

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Fri Jul 24, 2020 6:45 am

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It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike returns home along the same route at an average speed of 45 miles per hour, how long does the return trip take?

A. 1 hour, 15 minutes

B. 1 hour, 20 minutes

C. 1 hour, 25 minutes

D. 1 hour, 30 minutes

E. 1 hour, 35 minutes

[spoiler]OA=B[/spoiler]

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Fri Jul 24, 2020 6:45 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike r

by deloitte247 » Sun Jul 26, 2020 9:45 am

$$Average=\frac{dis\tan ce}{time\ taken}$$
Distance between Mike's home and workplace=>
$$=40\ miles\ per\ hour\ \cdot\ 1\frac{1}{2}=40\cdot1.5=60\ miles$$
Mike returns home along the same route at an average speed of 45 miles per hour.
$$Time\ taken\ for\ return\ trip=\frac{dis\tan ce}{speed}=\frac{60miles}{45miles\ per\ hour}$$ $$=\frac{4}{3}hours$$
$$=1\frac{1}{3}hours$$
=> 1 hour 20 minutes

Answer = option B

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Re: It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike r

by GMATGuruNY » Tue Aug 11, 2020 11:10 am

VJesus12 wrote: ↑
Fri Jul 24, 2020 6:45 am
It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike returns home along the same route at an average speed of 45 miles per hour, how long does the return trip take?

A. 1 hour, 15 minutes

B. 1 hour, 20 minutes

C. 1 hour, 25 minutes
D. 1 hour, 30 minutes

E. 1 hour, 35 minute

(higher speed)/(lower speed) = 45/40 = 9/8
Rate and time have a RECIPROCAL RELATIONSHIP.
Since the speed home is 9/8 of the speed to work, the time home will be 8/9 of the time to work:
(8/9)(90 minutes) = 80 minutes = 1 hour 20 minutes

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike r

by Scott@TargetTestPrep » Sat Aug 15, 2020 4:03 am

VJesus12 wrote: ↑
Fri Jul 24, 2020 6:45 am
It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike returns home along the same route at an average speed of 45 miles per hour, how long does the return trip take?

A. 1 hour, 15 minutes

B. 1 hour, 20 minutes

C. 1 hour, 25 minutes

D. 1 hour, 30 minutes

E. 1 hour, 35 minutes

[spoiler]OA=B[/spoiler]
Source: Princeton Review

Solution:

The distance between Mike’s home and his workplace is 40 x 1.5 = 60 miles. Therefore, the return trip takes 60/45 = 4/3 hours = 1 ⅓ hours = 1 hour 20 minutes.

Answer: B

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taniyuki: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon Oct 02, 2023 7:00 pm

Re: It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike r

by taniyuki » Mon Oct 02, 2023 7:03 pm

deloitte247 wrote: ↑
Sun Jul 26, 2020 9:45 am
$$Average=\frac{dis\tan ce}{time\ taken}$$
Distance between Mike's home and workplace=>
$$=40\ miles\ per\ hour\ \cdot\ 1\frac{1}{2}=40\cdot1.5=60\ miles$$
Mike returns home along the same route at an average speed of 45 miles per hour.
$$Time\ taken\ for\ return\ trip=\frac{dis\tan ce}{speed}=\frac{60miles}{45miles\ per\ hour}$$ $$=\frac{4}{3}hours$$
$$=1\frac{1}{3}hours$$
=> 1 hour 20 minutes

Answer = option B

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