Physics help?

Question

I need help finding the speed of an object if I was given the distance covered (160 km) and the average speed of the object (67.0 km/h). The objects speed during the first half of the distance is 88.0 km/h. Could anyone please explain how to find the speed of the second half of the distance?

Thanks. =)

Answer 1

Average speed is D(total)/t(total), not the average of the speeds for the two halves of the trip.

t1:
t1= D/v = 80/88 = 0.90909h

t2:
v(avg) = D/(t1 + t2)
v(avg)(t1 +t2) = D
v(avg)t1 + v(avg)t2 = D
v(avg)t2 = D - v(avg)t1
t2 = (D - v(avg)t1)/v(avg)
t2 = D/v(avg) - t1
t2 = 160/67 - 0.90909 = 1.4789h

v2 = (1/2)D/t2 = 80/1.4789 = 54.092Km/h