Friday, March 28, 2008

living 150 miles apart

Bryan and Kathleen live 150 miles apart. They each drive towards the other's house along a straight road connecting the two. Bryan drives at a constant rate of 30 miles per hour and Kathleen drives at a constant rate of 50 miles per hour. If Bryan and Kathleen leave their houses at the same time, how many miles are they from Bryan's house when they meet?

A. 40
B. 51.5
C. 56.25
D. 75
E. 93.75

3 comments:

Luís Botelho Ribeiro said...

Let S be the distance we seek in miles, say, the distance Bryan drives from home to the meeting point. She's driving more or less half the speed of Kathleen (maybe she's got a better a car or she's more anxious for the meeting than Bryan...).

We can already estimate the distance percurred by her will be a bit less than the double of Bryan's. We'll end out with something less than 100 miles for her and a bit more than 50 miles for him, as we have 150 miles for the total distance. This will be useful for a critic of the result we'll calculate next. So our options will probably be only B and C.

We can now choose one of two methods:

method A) test the two possible results, knowing that te meeting time is equal for both:

In option B. we have Bryan's time 51.5 / 30 = 1.71(6) HOURS. For the same situation Kathleen's time would be (150-51.5) / 50 = 1,97. Since this result is different from Bryan's time, we conclude option B. is not correct and we take C.


method B) Let us express in a equation the equality of metting time of Bryan and Kathleen:

S / 30 = (150 - S) / 50

solving this single variable equition, we get S = 56,25 miles, thus confirming option C. taken above.

A final remark: given the present day climate changes problem, probably we'd recommend Bryan and Kathleen to take some public transportation system if they definetely need to meet in person. If not, maybe a phone call, or an internet call through Voip or Skype would do...

Anonymous said...

it is really option C.

A - Brian
B - Kathleen
d(A,B)=150M (distance between A and B)
V(A)=30M/h (velocity of A)
V(B)=50M/h (velocity of B)
d(A)+d(b)=150M (sum of distance travelled)
V=d/t (equation in that velocity is equal to distance divided for time)

30=d(A)/t
50=d(B)/t ; t is equal for both because they leave their houses at same time and meet after a period of time that is equal for both either (the only variable is velocity). Therefore:
d(A)/30=d(B)/50, and
d(A)+d(B)=150

If we solve the system, we will come to the results:
d(B)=93,75M or distance travelled for Kathleen in order to Brian´s house
d(A)=56,25M or distance travelled for Brian

Anonymous said...

The two friends will meet after 1.875 hours (i.e. 150/(30+50)).

Therefore, Brian will drive for 56.25 miles (1.875*30).