Question

You travel 20.0 mph for 0.500 hour, 40.0 mph for 1.00 hour, 30.0 mph for 0.500 hour, and 50.0 mph for 2.00 hours. What is the average speed?

Answer 1

The answer is 41.25 mph.

The average speed (v) can be expressed as:
v = D/T  
where
D is total distance: D = d1 + d2 + d3 + d4
T is total time: T = t1 + t2 + t3 + t4

Now let's calculate distances using the formula: d = v * t:
d1 = v1 * t1 = 20.0 * 0.500 = 10 mi
d2 = v2 * t2 = 40.0 * 1.00 = 40 mi
d3 = v3 * t3 = 30.0 * 0.500 = 15 mi
d4 = v4 * t4 = 50.0 * 2.00 = 100 mi

Thus, the average speed is:
$v= \frac{D}{T}= \frac{d1 + d2 + d3 +d4}{t1+t2+t3+t4} = \frac{10+40+15+100}{0.500+1.00+0.500+2.00}= \frac{165}{4} = 41.25 mph$