ERJ Brainteaser: April

On his regular 2km commute, Barry took three minutes to cycle to work with the wind directly behind him, and returned home in four minutes, cycling against the same wind-force. How long would his total commuting time have been if there was no wind?

Answer: This week, the yellow jerseys (see Solutions below) go to: John Bowen, consultant, Bromsgrove, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Bharat B Sharma, technical director, Rajsha Chemicals Pvt. Ltd, (TWC Group), Vadodara (Guj) India; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Alfred Johnson, AlMailem Tires, Kuwait. Well done to everyone else who had a go.

SOLUTIONS

John Bowen

We need to use the basic equation of motion and set up 2 simultaneous equations and assume that the effects of the wind, when blowing, are equal and opposite in effect..

Into work, distance is 2km, time taken is 3 minutes with wid behind, so let cycling speed = V, wind speed effect = W, so

[V + W] =2/0.05 = 40km/hr     [Velocity = Distance/Time

And after work, time taken is 4 minutes against the wind

[V - W] =2/0.066666 = 30 km/hr

Adding these 2 equations, 2V = 70, so V = 35km/hr.

So, his total commuting time in the absence of wind = Distance/Time = 4km/35km/hr = 0.11426hours or 6,857minutes or 6minutes51.4seconds

Kamila Staszewska

To work, with wind: 2 km in 3 min (0.05h),  Speed= 2/0.05=40km/h (v+ w); v – Barry’s speed and w - wind,

To home, against wind: 2km in 4 min (0.0666h), Speed=2/0.0666=30km/h (v – w)

Barry’s speed without wind: (v+w)+(v-w)=2v=40+30; v=35km/h

Time of travel both ways without wind = 4km / 35km/h = 0.114h=6min51s

Sudi Sudarshan

Let S be the speed of the bike without wind and W the wind speed.

On the trip to school, relative speed is S+W

S+W  = Distance/Time = 2 / 3 Km per second

On the return trip, relative speed is S-W

S-W = Distance/Time = 2/4 = 1/2 Km per Minute

Adding the two equations:

2S  = 2/3 + 1/2 = 7/6

S = 7/12 Km per Minute

Total distance for the roundtrip = 4 Km

Time for the entire commute without wind  = Distance/Speed = 4/(7/12) = 48/7 = 6.86 Minutes or 6 minutes 51.4 seconds

Bharat B Sharma

Say Cycling speed is xmet/min

and wind speed is  y met/min

With wind in favour 3x+3y=2000

       12x+12y=8000

    (#1)     Multiplying by 4

With wind against 4x-4y=2000

       12x-12y=6000

     (#2)... Multiplying by 3

Adding both equation #1 &#2

24X= 14000

 Speed x = 14000/24 =

583.3333333

m/min

Total distance for return trip = 4000m (2 km each way)  

With no air speed, the time required will be distance/speed

6.857142857 minutes.

Amparo Botella

The time to get home with no wind will be 3,428 minutes.

V= speed with no wind (km/min)

W=speed with wind (km/min)

With wind: V+W=2/3Without wind: V-W=1/2

Then:

(V+W)+(V´W) = 2/3+1/2

2V=7/6

V=7/12 km/min.

To calculate the time to make 2 km.:

Time = 2/V = 2/(7/12) = 24/7 minutes = 3,428 min.

Alfred Johnson

C = Cycling Speed without wind

W = Wind Speed

Distance / Time = Speed

2 Km / 3 Min = C + W

2 Km / 4 Min = C - W

======================

 0.666 + 0.50 = C + W + C - W

C = 0.583 Km / Min

Answer : Barry could have taken 4 Km / 0.583  = 6.861 Min = 6 Min 51 Sec to complete the trip without wind, instead of 7 Mins.

0.5 Km / Min! That's quite fast! :)

Please note: Due to the UK Easter holidays the next teaser will be issued Tuesday 22 April.

2nd of May

7th of September

4th of March

?

Answer: As easy as ABC(D) once you saw the connection... but also a couple of great alternative answers (see Solutions). Very well done: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Jim Cristiano, director, category management, Veritas + HDT Automotive Solutions LLC, world headquarters, Livonia, Michigan, USA; Hans-Bernd Luechtefeld, consultant, Germany; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Ian Brooker, Sr. buyer, HB Chemical Corp., a Ravago company, Twinsburg, Ohio, USA; David Mann, Polymer Business Development consultant, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain.

SOLUTIONS

Andrew Knox

Answer: 1st of December (a, b, c, d,...).

Hans-Bernd Luechtefeld

1st of December,

According to the following logic:

2nd letter in May is 'A', 7th in September is 'B' and 3rd in March is 'C'. Now, looking for a Month with 'D', following the alphabetical order is December only, with the first letter.

Jim Cristiano

2nd of May - 2nd letter is A

7th of September - 7th letter is B

4th of March - 4th letter is C

1st of December - 1st letter is D

Sudi Sudarshan

Solution:  Each entry refers to the position of a letter in the word representing a month.

2nd of March refers to the letter a

7th of September refers to the letter b

4th of March refers to the letter c

In the order, the next letter of the alphabet is d.

December is the only month with the letter d, and it is the first letter of the word.

So 1st of December is the letter d

David Mann

If the pattern is 2nd letter of May (A) etc then the sequence is ABCD

The next one can only be 1st of December.

ALTERNATIVELY

Amparo Botella

If we follow the pattern that 2+2=4, 7+2=9 so the day could be 9th.

The same with the month, May (5) – March (3) = 2 so September (9) – 2 = 7 July.

Kamila Staszewska

The pattern is the following: the date is 7th of November