ASVAB Math Question: Sallu drove from Town A to Town B at an average speed of 20 mph.

[HaveAQUESTION]

My recruiter gave me something to take home to study the ASVAB. I got this study question wrong.

Sallu drove from Town A to Town B at an average speed of 20 mph. She then returned to Town A along the same road at an average speed of 30 mph. What was Sally's speed in miles per hour for the entire trip?

(A) 10

(B) 24

(C) 25

(D) 50

I picked C and was incorrect, and it said the correct answer is B. It didn't explain how B was the correct answer though. Can someone explain how can the answer be 24 and not 25.

 

[Deleted member 4993]

My recruiter gave me something to take home to study the ASVAB. I got this study question wrong.

Sallu drove from Town A to Town B at an average speed of 20 mph. She then returned to Town A along the same road at an average speed of 30 mph. What was Sally's speed in miles per hour for the entire trip?

(A) 10

(B) 24

(C) 25

(D) 50

I picked C and was incorrect, and it said the correct answer is B. It didn't explain how B was the correct answer though. Can someone explain how can the answer be 24 and not 25.

Assume that the distance between the towns = d miles

time taken to go up = d/20

time taken to come back = d/30

total time for travel = d/20 + d/30 = d/12

Average speed for travel = (2d)/( d/12) = 24

Remember that average of (1/2) and (1/4) is NOT (1/3)

 

[Dr.Peterson]

Sallu drove from Town A to Town B at an average speed of 20 mph. She then returned to Town A along the same road at an average speed of 30 mph. What was Sally's speed in miles per hour for the entire trip?

(A) 10

(B) 24

(C) 25

(D) 50

I picked C and was incorrect, and it said the correct answer is B. It didn't explain how B was the correct answer though. Can someone explain how can the answer be 24 and not 25.

To make it as simple as possible, suppose the distance from A to B is 60 miles. From A to B, it took 60/20 = 3 hours; from B to A it took 60/30 = 2 hours. That's a total distance of 120 miles in 5 hours, for an average speed of 120/5 = 24 mph. (It turns out that it doesn't matter what the actual distance is, as Khan showed algebraically.)

Why not (20 + 30)/2 = 25? Because she spent more time at the slower speed, so that contributes more to the average and "pulls it down".

Questions about average speed (and I wish the problem had used the word "average") must be calculated as "total distance / total time".