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# One day Andrew goes from his home to his school at a speed of 20 km/hr

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SVP
Joined: 08 Jul 2010
Posts: 1763
Location: India
GMAT: INSIGHT
WE: Education (Education)
One day Andrew goes from his home to his school at a speed of 20 km/hr [#permalink]

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19 May 2017, 11:38
00:00

Difficulty:

25% (medium)

Question Stats:

78% (03:10) correct 22% (01:56) wrong based on 36 sessions

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One day Andrew goes from his home to his school at a speed of 20 km/hr but on finding that it was holiday in school, he plans to have party with friends at a restaurant which is situated exactly at midpoint of his way from home to school so he starts back and reaches the restaurant at speed of 40 km/hr without wasting any time at school. Find the average speed of Andrew from home till he reaches restaurant after visiting school.

A) 24
B) 25
C) 30
D) 32
E) 35

Source: www.GMATinsight.com
[Reveal] Spoiler: OA

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Senior Manager
Joined: 22 Aug 2013
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Location: India
Re: One day Andrew goes from his home to his school at a speed of 20 km/hr [#permalink]

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19 May 2017, 11:54
Average Speed = (Total distance covered)/(Total time taken)

Let the distance from Andrew's home to school be d. Then distance from school to restaurant becomes d/2.

So, while going from home to school: Distance covered is 'd' and time taken is d/20
While coming back - from school to restaurant: distance covered is 'd/2' and time taken is (d/2)/40 = d/80

Thus, average speed = (d+d/2)/(d/20+d/80) = (3d/2)/(5d/80) = 24 Kmph.

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Re: One day Andrew goes from his home to his school at a speed of 20 km/hr [#permalink]

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20 May 2017, 00:19
Formula for average speed

Avg speed =$$\frac{(p+q)(a*b)}{bp + aq}$$

Let the distance to school from home be 2x.
Hence, the distance between the school and the halfway point(restaurant) is x.
The distances are in the ratio 2:1(p:q)

Also, we are given the respective speeds across these legs.
Here a is the speed from home to school : 20 miles/hour
b is the speed from school to restaurant : 40 miles/hour

Therefore, Average speed = $$\frac{(2+1)(20*40)}{(40*2 + 20*1)}$$
= $$\frac{(3)(20*40)}{100}$$ = 24(Option A)
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Joined: 26 Mar 2013
Posts: 1054
Re: One day Andrew goes from his home to his school at a speed of 20 km/hr [#permalink]

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20 May 2017, 03:10
GMATinsight wrote:
One day Andrew goes from his home to his school at a speed of 20 km/hr but on finding that it was holiday in school, he plans to have party with friends at a restaurant which is situated exactly at midpoint of his way from home to school so he starts back and reaches the restaurant at speed of 40 km/hr without wasting any time at school. Find the average speed of Andrew from home till he reaches restaurant after visiting school.

A) 24
B) 25
C) 30
D) 32
E) 35

Source: http://www.GMATinsight.com

Let total distance = 80 km

time from home to school = 80/20 = 4 hrs

time from school to restaurant = 40 / 40 = 1 hrs

Average speed = 120 / 5 = 24 km/hrs

Director
Joined: 04 Dec 2015
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Concentration: Technology, Strategy
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Re: One day Andrew goes from his home to his school at a speed of 20 km/hr [#permalink]

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20 May 2017, 04:12
One day Andrew goes from his home to his school at a speed of 20 km/hr but on finding that it was holiday in school, he plans to have party with friends at a restaurant which is situated exactly at midpoint of his way from home to school so he starts back and reaches the restaurant at speed of 40 km/hr without wasting any time at school. Find the average speed of Andrew from home till he reaches restaurant after visiting school.

Let the Distance from Home to School be D km.
Speed of Andrew from Home to School = 20km/hr
Thus Time taken to reach school from home = Distance / speed = $$\frac{D}{20}$$
Restaurant is exactly at midpoint from home to school, therefore Distance from school to restaurant = $$\frac{D}{2}$$km
Speed of Andrew from School to Restaurant = 40km/hr
Time taken to reach restaurant from school = $$\frac{D}{2}$$/40 = $$\frac{D}{80}$$

Average Speed = Total Distance Traveled / Total Time Taken
Average Speed of Andrew from Home till Restaurant = D + $$\frac{D}{2}$$ / $$\frac{D}{20}$$ + $$\frac{D}{80}$$ = $$\frac{2D + D}{2}$$ / $$\frac{4D + D}{80}$$ = $$\frac{3D}{2}$$/$$\frac{5D}{80}$$ = $$\frac{3}{2}$$ x $$\frac{80}{5}$$ = 24km/hr

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Re: One day Andrew goes from his home to his school at a speed of 20 km/hr [#permalink]

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20 May 2017, 12:42
GMATinsight wrote:
One day Andrew goes from his home to his school at a speed of 20 km/hr but on finding that it was holiday in school, he plans to have party with friends at a restaurant which is situated exactly at midpoint of his way from home to school so he starts back and reaches the restaurant at speed of 40 km/hr without wasting any time at school. Find the average speed of Andrew from home till he reaches restaurant after visiting school.

A) 24
B) 25
C) 30
D) 32
E) 35

Source: http://www.GMATinsight.com

let t=time from home to school
total distance=20t+40*t/4=30t
total time=t+t/4=5t/4
average speed=30t/(5t/4)=24 mph
A
Re: One day Andrew goes from his home to his school at a speed of 20 km/hr   [#permalink] 20 May 2017, 12:42
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