Speed and Distance.

Roland2rule 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

OA is D
Pls can an Expert give the mathematical breaKDOWN to this question? Thanks

I'd probably solve this the same way Erika did, but here's one alternative: fFirst, note that if he'd spent the same amount of time traveling at each respective speed, his average speed would have been 60mph. But we know he spent more time traveling at the faster speed, so we know he traveled at something faster than 60mph. A. B, and C are out.

Now we just need to test one of the remaining choices. If it works, it's the answer. If it doesn't work, the answer is the other one. Notice also, that the ratio of the times is 3:2 in favor of the faster speed. So if we were to plot the speeds on a number line, the respective distances from each speed to the overall average must work out to the same ratio.

Test D: 64
40-------------------64----------80
Gap:------24---------------16-------

Ratio of gaps: 24:16 = 3:2. That's what we want! So the answer is D