pkw209 wrote:Hey all,

Couldn't figure this one out. A brief explanation would be appreciated. Thanks!

76) Al, Pablo, and Masha shared driving on a 1,500 mile trip. Who drove greatest distance?

(1) Al drove 1 hr longer than Pablo but at an average speed of 5 mph slower than Pablo
(2) Masha drove 9 hrs and averaged 50 mph

I would recommend relying on commonsense and reasoning in addition to algebra here.

(2) is easier to evaluate, so let's look at that one first:

(2) Masha drove 9 hrs and averaged 50 mph.

This allows us to compute the distance Masha travelled (9*50 = 450) but since it's less than half the total distance, we can't say who drove the greatest distance. (That is, we still have 1500 - 450 = 1050 miles to spread around Al and Pablo. It could be Al driving for 1000 with Pablo driving for 50, or the other way around).

Insufficient.

(1) Al drove 1 hr longer than Pablo but an average speed of 5 mph slower than Pablo.

This information is not specific enough to allow us to determine distances that either Al or Pablo drove. It isn't even specific enough to allow us to figure out the times or speeds of Al and Pablo. And, of course, there is no info about Masha. Definitely insufficient.

In combination, you know from (1) that Al and Pablo combined for 1050 miles. From (2), you have expressions for Al and Pablo's distances:

(Sp - 5)*(Tp + 1) + (Sp)*(Tp) = 1050....[(Sp -5)*(Tp + 1) represents Al's distance]

We have to think about whether Al's or Pablo's distance is greater (that is, (Sp - 5)*(Tp +1) vs. (Sp)*(Tp)). You can reason that, depending on the numbers you pick, you can have either Al or Pablo travelling a greater distance. Alternatively, you can actually pick numbers to show this to yourself. But if you are actually going to pick numbers, you still have to reason a bit. If the speeds are very fast, then the fact that Al travels 5mph slower will surely be compensated by the extra hour he travels for, and so Al should travel a greater distance; conversely, if the speeds are very slow, then Pablo will travel a greater distance.

Choose E.

Thanks. I was down to C or E and my reasoning was that I thought there was only one combination of numbers that would satisfy the 1050 for Al and Pablo. I unfortunately forgot to take into account that either Al or Pablo could have driven the greater distance!