Hi LaxAvenger,
This type of multi-part rate question is something that you'll likely see at least once on Test Day. The difficulty level will vary depending on when it shows up and how well you're performing.
Since the language "hints" that we'll need the Distance Formula (references to distance, speed and time), we can start there....
Distance = (Rate)(Time)
The first part of the prompt tell us nothing special about the Rate and the Time, but DOES tell us that the distance is HALF of 240 miles.
120 mi. = (R)(T)
The second part of the prompt tells us the Rate increases by 10mph and the Time decreases by 1 hour for the second half of the trip....
120 mi. = (R+10)(T-1)
We're asked for the SPEED during the SECOND HALF of the trip.
At this point, we have 2 variables and 2 unique equations, so you COULD do "system math" and solve the problem that way. You COULD also TEST THE ANSWERS (as you did). Here though, we're given a subtle "pattern matching" shortcut. It's interesting that ALL of the numbers involved are ROUND NUMBERS (even the answer choices are all round numbers). When a question is based on lots of multiplication and division, IF all of the numbers involved are "nice" INTEGERS, then there's most certainly some type of relationship among the numbers.
I'm going to focus on the 2 Rates. They differ by 10 AND they both divide (probably EVENLY) into 120. I'd be thinking about 10 and 20, 20 and 30, 30 and 40. NEXT, we know that the difference in Times is just 1 hour....
10mph and 20mph would be a difference of 6 hours
20mph and 30mph would be a difference of 2 hours
30mph and 40mph would be a difference of 1 hour. THAT's exactly what we're looking for. No complex math required.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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