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# A man travels 120 miles by ship, 450 by train and 60 by car

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A man travels 120 miles by ship, 450 by train and 60 by car [#permalink]

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21 Dec 2011, 06:33
A man travels 120 miles by ship, 450 by train and 60 by car taking altogether 13 hours and 30 minutes for the entire journey. The speed of the train is 3 times that of the car and 1.5 times that of the ship. Find the speed of the train.

speed of car = x miles/hr
speed of ship=2x miles/hr
speed of train = 3x miles/hr

soln 1:

Total distance travelled=120+450+60=630 miles
Total time = 13.5 or 27/2 hours
Total speed = 6x miles per hour

hence 6x *27/2 = 630

x= 70/9
hence speed of train (3x)=70/3 or 23.3

Soln 2 :

Time taken by the train = distance/speed = 450/3x or 150/x
ship=120/2x or 60/x
car =60/x

since the total time ix 27/2 we can equate them

150/x+60/x+60/x=27/2
270/x=27/2 ---> x = 20

hence speed of train (3x) = 60 m/hr

why am i getting 2 different solns ? which method is wrong and why ..

Last edited by Bunuel on 25 Oct 2013, 09:16, edited 1 time in total.
RENAMED THE TOPIC.
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Re: Rate,distance,time - which method is correct?? [#permalink]

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21 Dec 2011, 07:14
rvinodhini wrote:
A man travels 120 miles by ship,450 by train and 60 by car taking altogether 13 hrs 30 min for the entire journey. The speed of the train is 3 times that of the car and 1.5 times that of the ship.Find the speed of the train.

speed of car = x miles/hr
speed of ship=2x miles/hr
speed of train = 3x miles/hr

soln 1:

Total distance travelled=120+450+60=630 miles
Total time = 13.5 or 27/2 hours
Total speed = 6x miles per hour

hence 6x *27/2 = 630

x= 70/9
hence speed of train (3x)=70/3 or 23.3

The first solution is the one that's incorrect. I highlighted the mistake in red. You just added the three speeds to find what you've called the 'total speed', and then used it as if it were the average speed. You do not add speeds together to find average speed - for example, If you travel, say, 20 mph by car, then 60 mph by train, your average speed will never be 80 mph. It will be somewhere between 20 and 60 mph.
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Re: Rate,distance,time - which method is correct?? [#permalink]

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21 Dec 2011, 07:23
Quote:

The first solution is the one that's incorrect. I highlighted the mistake in red. You just added the three speeds to find what you've called the 'total speed', and then used it as if it were the average speed. You do not add speeds together to find average speed - for example, If you travel, say, 20 mph by car, then 60 mph by train, your average speed will never be 80 mph. It will be somewhere between 20 and 60 mph.

Oops ..I get it know ... Thanks Stewart

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Re: Rate,distance,time - which method is correct?? [#permalink]

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21 Dec 2011, 07:31
how do you find speed of the ship: 2x?
edited: never mind. i got it
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Re: Rate,distance,time - which method is correct?? [#permalink]

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25 Oct 2013, 09:02
BDSunDevil wrote:
how do you find speed of the ship: 2x?
edited: never mind. i got it

Great question.

I still don't get why the speed of the ship is 2x.
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Re: Rate,distance,time - which method is correct?? [#permalink]

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25 Oct 2013, 09:21
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waltiebikkiebal wrote:
BDSunDevil wrote:
how do you find speed of the ship: 2x?
edited: never mind. i got it

Great question.

I still don't get why the speed of the ship is 2x.

Say the speed of the car is x miles per hour.

The speed of the train is 3 times that of the car --> the speed of the train is 3x miles per hour.
The speed of the train is 1.5 times that of the ship --> 3x=1.5*(speed of the ship) --> (speed of the ship)=3x/1.5=2x.

Hope it's clear.
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Re: Rate,distance,time - which method is correct?? [#permalink]

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25 Oct 2013, 09:24
Bunuel wrote:
waltiebikkiebal wrote:
BDSunDevil wrote:
how do you find speed of the ship: 2x?
edited: never mind. i got it

Great question.

I still don't get why the speed of the ship is 2x.

Say the speed of the car is x miles per hour.

The speed of the train is 3 times that of the car --> the speed of the train is 3x miles per hour.
The speed of the train is 1.5 times that of the ship --> 3x=1.5*(speed of the ship) --> (speed of the ship)=3x/1.5=2x.

Hope it's clear.

Yeah, ofc.

Now it makes sense!

Thank you.
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Re: A man travels 120 miles by ship, 450 by train and 60 by car [#permalink]

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07 Mar 2014, 00:36
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$$\frac{120}{2x} + \frac{450}{3x} + \frac{60}{x} = 13.5$$

Solving this, 3x = 60 = Speed of train.

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Re: A man travels 120 miles by ship, 450 by train and 60 by car [#permalink]

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07 Mar 2014, 18:42
Ratio of speeds is given:
T=3x
C=x
S=2x
To calculate:3x or x
Total time taken=Total Dist. By resp modes/speed of diff. Modes
13.5=450/3x + 120/2x + 60/x
X=60 on simplification

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Re: A man travels 120 miles by ship, 450 by train and 60 by car   [#permalink] 07 Mar 2014, 18:42
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