GMAT Math

Two women start walking toward each other from two ends of a bridge at the same time. They both leave at dawn. When they meet, it is 12pm. When the first woman reaches the other end of the bridge, it is 4pm. When the second woman reaches the other end of the bridge, it is 9pm. They both walk at constant, but different, rates. What time is dawn?

Help please!

awilhelm wrote:Two women start walking toward each other from two ends of a bridge at the same time. They both leave at dawn. When they meet, it is 12pm. When the first woman reaches the other end of the bridge, it is 4pm. When the second woman reaches the other end of the bridge, it is 9pm. They both walk at constant, but different, rates. What time is dawn?

Help please!

Please refer to the above image

Let F and S be the rates at which First and Second women are travelling. Let First woman start from A and Second woman from B and let them meet at 12 at C. Also assume that First and Second women were travelling for X hours when they met


From the pic,

X*F= 9S (Since the second woman travelled for 9 more hours to cover what the first woman traveled in X hours)
similarly
X*S = 4F



F= 9/X*S

Substituting this in the second equation

X*S = 4*9/X*S

X^2 = 36

X= 6

Both the travelers were travelling for 6 hours when it was 12. So they must have started at 6 hence the dawn is at 6 in the morning

is that a GMAT question?

Another solution:

x/9 = 4/x <=> x^2 = 36 and x = 6

• The left side of the equation: the first woman needs x hours for the distance for which the second woman needs 9 hours.
  The right side of the equation: the first woman needs 4 hours for the distance for which the second woman needs x hours.