Question

nikita ran a 5-kilometer race in 39 minutes (0.65 of an hour) without training beforehand. in the first part of the race, her average speed was 8.75 kilometers per hour. for the second part of the race, she started to get tired, so her average speed dropped to 6 kilometers per hour. which expression represents nikita’s distance for the second part of the race?

Answer 1

Total distance 5 km; at 5km / 0.65 h =

Second part distance: x; at 6 km/h, during t2

First part distance: 5 - x; at 8.75 km/h, during t1

V = d/t ⇒ t = d/V

t2 = x/6
t1=[5-x]/8.75

t2 + t1 = 0.65

x/6 + [5-x]/8.75 = 0.65

x/6 + 5/8.75 - x/8.75 = 13/20

x/6 - x/8.75 = 13/20 - 5/8.75

x/6 - 4x/35 =13/20 - 20/35

35x - 24x = (35*6)(35*13 - 20*20)/(20*35)

11 x = 16.5
x = 16.5/11 = 1.5 km