Problem Solving

Steve traveled the first 2 hours of his journey at 40 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?

A. 60 mph
B. 56.67 mph
C. 53.33 mph
D. 64 mph
E. 66.67 mph

The OA is D.

I'm confused by this PS question. Experts, any suggestion, please? Thanks in advance.

LUANDATO wrote:Steve traveled the first 2 hours of his journey at 40 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?

A. 60 mph
B. 56.67 mph
C. 53.33 mph
D. 64 mph
E. 66.67 mph

2 hours are spent at 40mph.
3 hours are spent at 80mph.
Average speed for all 5 hours = (2*40 + 3*80)/5 = 320/5 = 64.

The correct answer is D.

LUANDATO wrote:Steve traveled the first 2 hours of his journey at 40 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?

A. 60 mph
B. 56.67 mph
C. 53.33 mph
D. 64 mph
E. 66.67 mph

The OA is D.

I'm confused by this PS question. Experts, any suggestion, please? Thanks in advance.

Mitch's and Dan's approach is probably simplest. But here's a fun alternative:

If Steve had spent the same amount of time traveling at each speed, his average would have been right in the middle of 40 and 80, or 60mph. We know he spent more time traveling at the faster speed, and thus, his average must be more than 60. That leaves us D and E.

Now we can test one of the two remaining choices and see if we get a 3:2 ratio in favor of time spent traveling at 80mph.
Test D: 64
Plot the rates on a number line:
40-----------------64-----------80
Gaps:-------24----------16--------
Ratio of time spent at 80 mph to 40 mph: 24:16 = 3:2. And we've got our answer.