Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 30 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)

The strategy guide does NOT go over how they get from the set up to setting the times equal to each other 30/r = [(30/(r+5))+(1/15)].

I understand how the guide gets to this point BUT I need someone to explain the rational behind setting the times equal to each other.

What in the problem prompts this set up? It will be easier for me to remember if I understand the logic behind it.

Thank you in advance!

Good question! I completely agree that we learn better when we understand the logic behind something.

I do want to get an equation at some point so that I have something to solve. The two timeframes actually don't equal each other at this point - while speeding, Liam gets there 4 minutes early, but if he hadn't sped, then he'd have gotten there exactly on time. So what do I need to adjust in order to make those two timeframes equal?

Hmm. Speeding took 4 minutes less than not speeding. How would i make those two times equal? Add 4 minutes to the faster time - the speeding time. Then that'll equal the slower time - the time it would've taken when NOT speeding.

so I've got:
non-speeding time = speeding time + 4 minutes
Oh, but how annoying - the speeding and non-speeding times were given in terms of hours, not minutes (because the rates were miles per hour). So I can't just use +4. I have to convert minutes to hours.

4m * (1h / 60m) = (1/15) hour
so I'll use 1/15 in the equation instead.

Does that make more sense now? :)

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT