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 kmAnswer E

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"