Expert: Ahmed Salami - 4/10/2009

Question
QUESTION: On the response given in the problem of Bob Rodriquez who is trying to get to NY and trying to figure out what was faster, friend or train.
Q1. The answer given in the first part was 156/80= 39/20 I see it was divided by 4. How? or why?
Q2. The second part 39/20 + 1/2 = 49/20, how?

ANSWER: Hi Michael,
I'm lost here. What response?

---------- FOLLOW-UP ----------

QUESTION: Bob Rodriquez, the Albany, NY sales representative for Advanced Drafting Software, Inc., must attend the regional sales meeting in New York City.  Unfortunately, his car is in the shop so he must make other travel arrangements to reach his destination.  One option is to take a train that departs at 8:00 A.M.  Alternatively, he could ride to the meeting with another sales rep.

Bob has an important presentation to deliver at the meeting and needs to arrive as early as possible.   He knows that the train travels at 80 miles per hour, but has a 30 – minute layover halfway through the 156-mile trip.  He also knows that his friend cannot depart before 8:00 A.M. and will adamantly refuse to drive any faster than 55 miles per hour.

If both methods of transportation leave at the same time (8:00 A.M.), will the train or the car allow him to reach the regional sales meeting sooner?


Answer
Hi Michael,
For a 156-mile trip, moving at 80 miles/hr results in spending
156/80 hrs = 39/20 hrs
we've divided both top and bottom here by 4 because it is the highest common factor of both. Its just simplification. You could have divided by 2 and gotten 78/40 and you'll find out that you can still divide by 2 again to get 39/20. You have to note that we havent divided the quantity by 4, we have only simplified it by doing the same thing to both the numerator and denominator. And of course, a calculator would confirm that 156/80 and 39/20 are in fact the same quantity.
39/20 hrs is the time spent while the train is moving, because of the 1/2 hr layover during the trip the total time spent on the journey is therefore
39/20 + 1/2 = 39/20 + 10/20
         = (39 + 10)/20
         = 49/20
In case you're still wondering which of the modes is faster, well, the friend would spend 156/55 which is more than 49/20.

Regards