# The Naked Scientists Forum

### Author Topic: Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours and 11 minutes?  (Read 1030 times)

#### thedoc

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##### Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours and 11 minutes?
« on: 17/05/2016 11:50:02 »
Colin Tshivhase  asked the Naked Scientists:
Dear Chris
Please advise on the probability and the speed you need to travel at to achieve driving time of 2h11minutes based on below scenario.
A Trip from Midrand South Africa to Makhado Town ( Louis Trichardt)  South Africa which is approximately 400km. The name of the national road is N1  highway and it's a double lane road . There is 4 tollgate a along the way that you need to stop and pay. The legal speed limit is 120 km per hour and he claims to have started the trip at 3h30 am
We have been arguing since last week that it is impossible to achieve 2h11 minutes

What do you think?
« Last Edit: 17/05/2016 11:50:02 by _system »

#### chiralSPO

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##### Re: Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours a
« Reply #1 on: 17/05/2016 12:52:13 »
going 400 km in 2.18333 hours works out to an overall rate of about 180 km/hour. Including 4 toll stations and a possible traffic jam somewhere along the way, one would probably need to reach a top speed of about 200 km/hour to achieve this average.

While this is not strictly impossible, it certainly does not abide by the speed limit!

#### PmbPhy

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##### Re: Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours a
« Reply #2 on: 17/05/2016 13:10:34 »
Quote from: Colin Tshivhase

A Trip from Midrand South Africa to Makhado Town ( Louis Trichardt)  South Africa which is approximately 400km. The name of the national road is N1  highway and it's a double lane road . There is 4 tollgate a along the way that you need to stop and pay. The legal speed limit is 120 km per hour and he claims to have started the trip at 3h30 am
We have been arguing since last week that it is impossible to achieve 2h11 minutes
If I were you I'd solve the problem without considering the tolls and assume that the cars are moving at a constant speed of 120 km/h. This way the time to consider the tolls is probably small enough to ignore. Therefore simply find the time by solving for T in the relation v = D/T => T = D/v = (400 km)/(120 km/h) = 3h. That's the shortest time it would take to travel 400 km at 120 km/h. Therefore if one doesn't stop for tolls it still couldn't travel 400 km in 2h11m.

What I don't understand is why you were unable to determine this yourself? It's a basic algebra problem. Perhaps you don't know algebra?

#### McQueen

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##### Re: Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours a
« Reply #3 on: 17/05/2016 14:19:36 »
Therefore simply find the time by solving for T in the relation v = D/T => T = D/v = (400 km)/(120 km/h) = 3h. That's the shortest time it would take to travel 400 km at 120 km/h. Therefore if one doesn't stop for tolls it still couldn't travel 400 km in 2h11m.

The brilliance is quite blinding. Can't see the tree for the woods in this effulgence!

#### syhprum

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##### Re: Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours a
« Reply #4 on: 17/05/2016 20:09:02 »
This is a very simple arithmetic problem rather out of place in a forum discussing Physics, Astronomy & Cosmology.

#### alancalverd

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##### Re: Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours a
« Reply #5 on: 17/05/2016 22:28:58 »
It is also one of the very few sensible questions raised in the last month.

400 km in 131 minutes = 3.053 km/minute or 183.2 kph, somewhat above the speed limit.

#### evan_au

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##### Re: Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours a
« Reply #6 on: 18/05/2016 11:21:35 »
Google Maps estimates 4 hours 2 minutes for this trip.
Since it is generally north-south, I assume it is not crossing some time zone boundary?
And it didn't take place at the end of Daylight Savings (which happened recently in the southern hemisphere)?

#### The Naked Scientists Forum

##### Re: Please solve our argument: at what speed would you need to travel to cover 400 km's in 2 hours a
« Reply #6 on: 18/05/2016 11:21:35 »