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Speed and Distance.

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Speed and Distance.

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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

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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

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To find average speed for the whole trip, we need to find 1) total distance for the whole trip and 2) total time for the whole trip. We can then divide total distance by total time to get total speed for the whole trip (since r = d/t).

If Steve traveled for 2 hours at 40 MPH, he went 80 miles. Then, if he traveled for 3 hours at 80 MPH, he went 240 miles. That gives 320 miles in total. We can also add up that he traveled 2 + 3 = 5 hours in total.

Now that we have total distance for the whole trip and total time for the whole trip, we can divide distance by time to get speed: $$\frac{320\ miles}{5\ hours}=\ 64\ mph$$

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