Speed equation

Question

a pilot traveled the first 1 500 miles of a 3 000 journey with an average speed of 400 mph at what speed must the pilot travel the remaining 1,500 miles to record an average speed of 500 mph or the entire flight

Answer 1

distance=rate*time

d=r*t

total distance=rate*total time

3000=500*t

t=3000/500

t=6 hours total time

find the time for the first part of the trip

1500=400*t

1500/400=t

3.75=t

3.75 hours is the time for the first part of the trip

that leaves 6-3.75=2.25 hours for the second part of the trip

now find the rate for the second part of the trip

t=2.25 hours and d=1500 miles

d=r*t

1500=r*2.25

r=1500/2.25

r=666.666... mph is the rate for the second part of the trip to give you an average speed of 500 mph

notice that the answer is not 600 mph; this is because the amounts of time are different for each of the two parts of the trip; more time is spent travelling 400 mph during the first part of the trip-that is why the average of 500 mph is closer to 400 mph than to 666.666...mph