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# At 12:00 hour a truck left the city A to city B, at a consta

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Intern
Joined: 15 Jun 2010
Posts: 9
At 12:00 hour a truck left the city A to city B, at a consta  [#permalink]

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15 Apr 2014, 14:26
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Difficulty:

25% (medium)

Question Stats:

79% (01:34) correct 21% (02:11) wrong based on 165 sessions

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At 12:00 hour a truck left the city A to city B, at a constant speed of 45 km/h. One hour later, a car left the city B to the city A, along the same road, at a constant speed of 100 km/h. If the distance between A and B is 190 km, at what time will the truck and the car meet each other?

A. 12:40
B. 13:00
C. 14:00
D. 14:40
E. 16:00
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Re: At 12:00 hour a truck left the city A to city B  [#permalink]

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15 Apr 2014, 19:34
1
tauchmeister wrote:
I'm having some problems with the following question:

At 12:00 hour a truck left the city A to city B,
at a constant speed of 45 km/h. One hour later,
a car left the city B to the city A, along the same
road, at a constant speed of 100 km/h. If the
distance between A and B is 190 km, at what
time will the truck and the car meet each other?
a) 12:40
b) 13:00
c) 14:00
d) 14:40
e) 16:00

Official answear is C

It's best to draw a diagram in these questions to help you see the situation.

A ____45______T (1:00)_____________145____________ B

The truck starts from A at 12:00 and reaches a point, T, 45 km away in 1 hour i.e. at 1:00 because the speed of the truck is 45 km per hour.
Since total distance between A and B is 190 km and the truck has already covered 45, the distance between T and B is 190 - 45 = 145 km.

Now, at 1:00, truck starts from T and Car starts from B and they travel towards each other at a relative speed of 45 + 100 = 145 km/hr (since they are moving in opposite directions, relative speed is the sum of their speeds)

To cover a distance of 145 km at a relative speed of 145 km/hr, they will take 145/145 = 1 hour.

So they will meet 1 hour after 1:00 i.e. at 2:00.

For more on relative speed, check: http://www.veritasprep.com/blog/2012/07 ... elatively/
http://www.veritasprep.com/blog/2012/08 ... -speeding/
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Re: At 12:00 hour a truck left the city A to city B  [#permalink]

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15 Apr 2014, 21:21
At 1300 Hrs, truck has already travelled 45 Kms & car has started from City B

Distance remaining = 190 - 45 = 145

Setting up the equation

Lets say truck travels x kms & meets car

$$\frac{x}{45} = \frac{145-x}{100}$$

29x = 145 * 9

x = 45

To travel 45Kms, truck would again require 1 hr

So they would meet at 1400 Hrs

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Re: At 12:00 hour a truck left the city A to city B  [#permalink]

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15 Apr 2014, 21:46
1
Car started from City B one hour after the truck. So, distance traveled by the truck going at 45 KM/H in this one hour = 45 KM
Distance left to be covered between the car and the truck = 145 KM
Relative speed of the car and truck combined = 100 KM/H + 45 KM/H = 145 KM/H
Time taken to cover this pending distance(D/S) = 145/145 = 1 H

So total time taken = 1H (truck's headstart) + 1H (from prev step) = 2H. So time they met = 12 + 2 = 14.00 Hrs.
Manager
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Re: At 12:00 hour a truck left the city A to city B, at a consta  [#permalink]

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20 Apr 2014, 20:30
Let after t hour they will meet
45t+100(t-1)=190 so, t=2 Ans C
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At 12:00 hour a truck left the city A to city B, at a consta  [#permalink]

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31 Aug 2015, 06:40
1
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

At 12:00 hour a truck left the city A to city B, at a constant speed of 45 km/h. One hour later, a car left the city B to the city A, along the same road, at a constant speed of 100 km/h. If the distance between A and B is 190 km, at what time will the truck and the car meet each other?

A. 12:40
B. 13:00
C. 14:00
D. 14:40
E. 16:00

==> this is a common velocity question in gmat math test. remember that here, the same time flows the situation.
in case of A truck, it travels at the speed of 45km/h, thus it traveled 45km after 1 hour.
In case of A car, it travels at the speed of 100km/h, and since it started traveling at 13:00, we have 45+45T+100T=190.(It's not the separate t1, t2 here because the same time flows for both the car and truck. Therefore it's just T.)
145T=145, T=1 and therefore at 14:00, the truck and car meet. C is the answer.

If you know our own innovative logics to find the answer, you don’t need to

actually solve the problem.
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At 12:00 hour a truck left the city A to city B, at a consta   [#permalink] 31 Aug 2015, 06:40