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)

1 answer

To find an expression for Nikita’s distance during the second part of the race, we first need to determine how much time she spent on each part of the race.

Let:

  • \( t \) = time spent in hours during the first part of the race.
  • The remaining time for the second part of the race will be \( 0.65 - t \) hours (since the total race time is 0.65 hours).

In the first part of the race, she ran at an average speed of 8.75 km/h:

  • The distance for the first part of the race is given by \( \text{distance} = \text{speed} \times \text{time} \). So, the distance for the first part is: \[ \text{Distance}_{\text{first part}} = 8.75t \]

For the second part of the race, her speed dropped to 6 km/h. The time spent in this part is \( 0.65 - t \) hours:

  • Therefore, the distance for the second part is: \[ \text{Distance}_{\text{second part}} = 6(0.65 - t) \]

This means that the expression that represents Nikita’s distance for the second part of the race is: \[ 6(0.65 - t) \]

Thus, the answer is 6(0.65 - t).