Problem Solving

REINE wrote:Adam and Beth each drove from a Smallville to Crowncity by different routes. Adam drove an average speed of 40miles/hour and completed the trip in 30 minutes. Beth's routes was 5 miles longer, and it took her 20 minutes more than Adam to complete the trip. How many miles per hour was Beth's average speed of the trip.
A. 24
B. 30
C. 48
D. 54
E. 75

Adam drove an average speed of 40 miles/hour and completed the trip in 30 minutes
Distance = (rate)(time)
= (40 mph)(0.5 hours)
= 20 miles.
So, ADAM drove 20 miles

Beth's routes was 5 miles longer, and it took her 20 minutes more than Adam to complete the trip.
Since Adam drove 20 miles, we know that Beth's TRAVEL DISTANCE = 25 miles
Since Adam drove for 30 minutes, we know that Beth's TRAVEL TIME = 50 minutes = 5/6 hours

How many miles per hour was Beth's average speed of the trip.
Average speed = (TOTAL DISTANCE)/(TOTAL TIME)
= 25/(5/6)
= (25)(6/5)
= 30 miles per hour

Answer: B

Cheers,
Brent

Hi REINE,

This question can be solved with a mix of arithmetic and TESTing THE ANSWERS.

We're told that Adam drove 40 mph for 30 minutes. That distance = (40 mph)(1/2 hour) = 20 miles. We're then told that Beth's trip was 5 miles LONGER and 20 minutes MORE to complete - so she traveled for 25 miles and drove for 50 minutes. We're asked for Beth's average speed.

Beth drove for ALMOST an hour; if she had driven for an hour, then she would have an average speed of 25 mph. Since she drove that distance in a little LESS than an hour though, she would have driven a little faster than 25 mph.

Let's TEST Answer B: 30 mph

If she drove 30 mph for 50 minutes, then the total distance traveled would have been (30 mph)(5/6 hour) = 150/6 = 25 miles. This is an exact match for what we were told, so this MUST be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich