If a car went the first third of the distance at 80 kmh

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

If a car went the first third of the distance at 80 kmh

by Gmat_mission » Sun May 06, 2018 10:58 am

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If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 44 kmh
E. 50 kmh

[spoiler]OA=B[/spoiler].

What is the formula that helps me to solve this PS question? I need some help here. Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Sun May 06, 2018 10:58 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Sun May 06, 2018 11:54 am

Hello Gmat_mission.

If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

Let call d the total distance. The average speed is equal to: (total distance )/ (total time). We have

$$\frac{d}{3}\cdot\left(\frac{1}{80}\right)$$ $$\frac{d}{3}\cdot\left(\frac{1}{24}\right)$$ $$\frac{d}{3}\cdot\left(\frac{1}{48}\right)$$ Therefore, $$Average\ speed=\frac{d}{3}\left(\frac{1}{80}+\frac{1}{24}+\frac{1}{48}\right)=\frac{d}{3}\left(\frac{3}{40}\right)=\frac{d}{40}.$$ this implies that the correct answer is the option B.

I hope it helps.

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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

by Brent@GMATPrepNow » Sun May 06, 2018 11:56 am

Gmat_mission wrote:If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 44 kmh
E. 50 kmh

Here's an algebraic approach:

Let d = 1/3 of the total distance traveled
So, the car traveled d km at 80 kmh, then the car traveled d km at 24 kmh, and then d km at 48 kmh

Average speed = (total distance traveled)/(total travel time)

Total distance traveled = d + d + d = 3d

time = distance/speed
Total time spent traveling = (time spent traveling 80kmh) + (time spent traveling 24 kmh) + (time spent traveling 48 kmh)
= d/80 + d/24 + d/48 [let's rewrite this with a common denominator]
= 3d/240 + 10d/240 + 5d/240
= 18d/240
= 9d/120
= 3d/40

Average speed = (3d)/(3d/40)
= 120d/3d
= 40

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sun May 06, 2018 1:48 pm

Gmat_mission wrote:If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 44 kmh
E. 50 km

Let each third of the distance = 240 km, implying that the total distance = 3*240 = 720 km.
Since the rate for the first third = 80 kmh, the time to travel the first third = d/r = 240/80 = 3 hours.
Since the rate for the second third = 24 kmh, the time to travel the second third = d/r = 240/24 = 10 hours.
Since the rate for the last third = 48 kmh, the time to travel the last third = d/r = 240/48 = 5 hours.
Average speed for the entire trip = (total distance)/(total time) = 720/(3+10+5) = 720/18 = 40 kmh.

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue May 08, 2018 3:17 pm

Gmat_mission wrote:If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 44 kmh
E. 50 kmh

We can let the total distance = 3d and create the equation:

average = 3d/(d/80 + d/24 + d/48)

average = 3d/(d/80 + d/24 + d/48)

average = 3d/(3d/240 + 10d/240 + 5d/240)

average = 3d/(18d/240)

average = 720d/18d = 40

Answer: B

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