Car A drives from P to Q at a constant rate of 100 km per ho

Max@Math Revolution 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

Since A's rate is 100 km per hour, the distance traveled by A in the first hour = 100 km.
Remaining distance between A and B = (total distance) - (distance traveled by A in the first hour) = 600-100 = 500 km.

When A and B drive toward each other, they WORK TOGETHER to cover the remaining 500 km between them.
When elements work together, ADD THEIR RATES.
The combined rate for A and B = 100+150 = 250 km per hour.
Of every 250 km traveled by A and B working together, 100 km are traveled by A.
Implication:
Car A travels 100/250 of the remaining 500 km:
(100/250) * 500= (2/5)(500) = 200 km.

Thus:
Total distance traveled by A = (100 km traveled in the first hour) + (remaining distance traveled by A) = 100+200 = 300 km.

The correct answer is E.

=>

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.