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Car A drives from P to Q at a constant rate of 100 km per hour. Afte

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Car A drives from P to Q at a constant rate of 100 km per hour. Afte  [#permalink]

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New post 04 Apr 2018, 01:55
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[GMAT math practice question]

Car A drives from P to Q at a constant rate of 100 km per hour. After car A has driven for 1 hour, train B begins traveling from Q to P at a constant rate of 150 km per hour. If the distance between P and Q is 600 km, then what distance has car A traveled when it meets train B?

A. 200 km
B. 220 km
C. 250 km
D. 270 km
E. 300 km

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Re: Car A drives from P to Q at a constant rate of 100 km per hour. Afte  [#permalink]

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New post 04 Apr 2018, 02:19
MathRevolution wrote:
[GMAT math practice question]

Car A drives from P to Q at a constant rate of 100 km per hour. After car A has driven for 1 hour, train B begins traveling from Q to P at a constant rate of 150 km per hour. If the distance between P and Q is 600 km, then what distance has car A traveled when it meets train B?

A. 200 km
B. 220 km
C. 250 km
D. 270 km
E. 300 km

A speed-100 km per hour
In one hour Car a travels 100km.
Distance left 500km.

Time at which both train and car meets=500/(100+150)=2
distance traveled by train= 2*150 =300.

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Car A drives from P to Q at a constant rate of 100 km per hour. Afte  [#permalink]

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New post 04 Apr 2018, 09:17
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MathRevolution wrote:
[GMAT math practice question]

Car A drives from P to Q at a constant rate of 100 km per hour. After car A has driven for 1 hour, train B begins traveling from Q to P at a constant rate of 150 km per hour. If the distance between P and Q is 600 km, then what distance has car A traveled when it meets train B?

A. 200 km
B. 220 km
C. 250 km
D. 270 km
E. 300 km

This problem has a couple of potential traps:
a) Distance between P and Q \(\neq\) Distance between A and B;
b) A's total distance depends on A's total travel time, including the one hour that A travels alone

1) Find actual distance between A and B
Total D between P and Q = 600 km
Actual D between A and B = 500 km
- A travels alone for 1 hour
- A travels (100 kmh * 1hr)= 100 km
- A travels toward B, shortens the distance
- (600-100) = 500km between them when B starts

2) Find time it takes for A and B to meet

Time=D/R, and D=500. We need rate (speed)
Opposite directions: ADD speeds of A and B
Combined speed = (100 + 150) = 250 kmh

Time to meet=D/R: \(\frac{500}{250}\)= 2 hours

3) Total distance that A has traveled?
Use A's total time, then multiply by A's rate

TOTAL time that A travels
Alone: 1 hour
To meet B: 2 hours
Total time A travels: 3 hours

TOTAL distance A travels, RT=D:
(100 kmh * 3 hrs) = 300 km

Answer E
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Re: Car A drives from P to Q at a constant rate of 100 km per hour. Afte  [#permalink]

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New post 04 Apr 2018, 10:21
MathRevolution wrote:
[GMAT math practice question]

Car A drives from P to Q at a constant rate of 100 km per hour. After car A has driven for 1 hour, train B begins traveling from Q to P at a constant rate of 150 km per hour. If the distance between P and Q is 600 km, then what distance has car A traveled when it meets train B?

A. 200 km
B. 220 km
C. 250 km
D. 270 km
E. 300 km


1 hour*100 kmh+[500/(100+150)] hours*100 kmh=300 km
E
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Re: Car A drives from P to Q at a constant rate of 100 km per hour. Afte  [#permalink]

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New post 05 Apr 2018, 23:51
=>

After car A has driven for 1 hour, the distance between car A and train B is 500 km.

Car A and train B approach each other at a speed of 250 km/hr. This means that they will take 2 hours to meet each other.
When they meet, car A will have traveled for 3 hours, and have covered a distance of 3 * 100 = 300 km.


Therefore, the answer is E.

Answer: E

It is important that both vehicles will have traveled for the same amount of time after train B has started moving. This gives the equation 100 + 100t + 150t = 600, from which we may deduce that t = 2. Since 100 + 100 *2 = 300, E is the answer.
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Re: Car A drives from P to Q at a constant rate of 100 km per hour. Afte  [#permalink]

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New post 14 Apr 2018, 21:46
MathRevolution wrote:
[GMAT math practice question]

Car A drives from P to Q at a constant rate of 100 km per hour. After car A has driven for 1 hour, train B begins traveling from Q to P at a constant rate of 150 km per hour. If the distance between P and Q is 600 km, then what distance has car A traveled when it meets train B?

A. 200 km
B. 220 km
C. 250 km
D. 270 km
E. 300 km


Speed of Car = 100 km/hr

Let us say time = t

Distance travelled by Car = 100t

Speed of Train = 150 km/hr

Time = t - 1

Distance travelled by Train = 150 (t - 1)

Total distance = 600 kms

So, 600 = 100t + 150t - 150

750 = 250t

t = 3

Therefore, distance travelled by Car when it meets Train = 3 * 100 = 300 kms

(E)
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Re: Car A drives from P to Q at a constant rate of 100 km per hour. Afte   [#permalink] 14 Apr 2018, 21:46
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