Two long time friends want to meet for lunch on a free weeke

[alanforde800Maximus]

Two long time friends want to meet for lunch on a free weekend. One friend Ann, lives in Portland, and the other, Bill, lives in Seattle. They decide to meet somewhere on the 200-mile stretch connecting the two cities, and they start driving simultaneously from their respective cities toward each other along the same route. Ann drives an average of 50 miles per hour, and Bill drives an average of 70 miles per hour. Approximately how many miles from Portland will the two meet?

a) 56.7
b) 60.0
c) 72.5
d) 83.3
e) 96.7

Please assist with above problem.

[[email protected]]

Hi alanforde800Maximus,

This is an example of a combined rate question. Since Ann drives at 50 miles/hour and Bill drives at 70 miles/hour, they travel a total of 120 miles each hour. The starting distance between them is 200 miles, so we can figure out how long it would take them to meet up...

D = (R)(T)
200 miles = (120 miles/hour)(Time)
200/120 = Time
5/3 hours = Time to meet

The questions how far they are from PORTLAND when they meet. Since Anne is traveling from Portland, and they meet after 5/3 hours, we can figure out how far Anne is from Portland...

D = (R)(T)
D = (50 miles/hour)(5/3 hours)
D = 250/3 miles
D = 83.33333 miles

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[crackverbal]

Hi alanforde800Maximus,

Another approach of solving Speed, Distance and Time questions is to figure out which one out of distance and time will be a constant (in most cases there will be one).

If the distance is constant then we use the equation S1T1 = S2T2

If the time is constant then we use the equation D1/S1 = D2/S2

Another good practice to follow is to always graphically represent the question as shown in the image.



Since the time is constant here

D(A)/S(A) = D(B)/S(B)
x/50 = (200-x)/70 -----> x = 83.3

[GMATGuruNY]

Two long time friends want to meet for lunch on a free weekend. One friend Ann, lives in Portland, and the other, Bill, lives in Seattle. They decide to meet somewhere on the 200-mile stretch connecting the two cities, and they start driving simultaneously from their respective cities toward each other along the same route. Ann drives an average of 50 miles per hour, and Bill drives an average of 70 miles per hour. Approximately how many miles from Portland will the two meet?

a) 56.7
b) 60.0
c) 72.5
d) 83.3
e) 96.7

Ann and Bill are WORKING TOGETHER to cover the 200 miles between them.
When people work together, ADD THE RATES.
The combined rate for Ann and Bill = 50+70 = 120 miles per hour.
Of every 120 miles traveled when Ann and Bill work together, Ann drives 50 miles.
Thus, she will travel 50/120 of the 200 miles:
(50/120)(200) = 83.33 miles.

The correct answer is D.