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

6(0.65 – t)

Explanation:

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?

6t

0.65 – t

6(0.65) – t

6(0.65 – t)

which the answer is 6(0.65 – t)

Answer 2

First part of the race

speed1, s1 = 8.75 km/h
distance1 = 5 km - x
time 1 = 0.65 h - t

Second part of the race

speed2, s2 = 6 km/h
distance2 = x
time2 = t

s2 = x/t = 6 ⇒ t = x / 6

s1 = [5 - x] / [0.65 - t] = 8.75

5 - x = 8.75 [0.65 - t]

5 -x = 8.75(0.65) - 8.75t

5 - x = 5.6875 - 8.75 (x/6)

5 - x = 5.6875 - 1.4583x

1.4583 x - x = 5.6875 - 5

0.4583 x = 0.6875

x = 0.6875 / 0.4583 = 1.5