If Lucy walks to work at a rate of 4 miles per hour

swerve wrote:If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour

The OA is C.

Please, can anyone explain this PS question? I tried to solve it but I can't get the correct answer. I need help. Thanks.

A quick approach is to assign a nice value to the distance from home to work.
That is, we want a distance that works well with the two speeds (4 mph and 6 mph)
Let's say the distance from home to work = 12 miles

Time TO work = distance/speed = 12/4 = 3 hours
Time FROM work = distance/speed = 12/6 = 2 hours
TOTAL time = 3 + 2 = 5 hours

TOTAL distance = 12 + 12 = 24 miles

Average speed = total distance/total time
= 24/5 miles per hour
= 4.8 miles per hour

Answer: C

Hi swerve,

Since this question gives us just the two rates to work with, we can solve it by TESTing VALUES.

The two speeds are 4 miles/hour and 6 miles/hour, so we should choose a common multiple of those two numbers for the one-way distance. Let's TEST 12 miles.

Walking to work:
D = (R)(T)
12mi. = (4 miles/hr)(X hours)
3 hours = X

Walking from work:
D = (R)(T)
12mi. = (6 miles/hr)(Y hours)
2 hours = Y

Total Distance = 12 + 12 = 24 miles
Total Time = 3 + 2 = 5 hours
Average Speed (round-trip) = 24/5 = 4.8 miles/hour

Final Answer: C

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

swerve wrote:If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour

We can use the equation:

average speed = (total distance)/(total time)

If we let distance each way = 12, we have:

Average = (12 + 12)/(12/4 + 12/6)

Average = 24/5 = 4.8 mph

Answer: C