Question

Anika traveled 448 km by car to visit her mother for the holidays. She drove part of the way at 43 km/h and the rest of the way at 81 km/h. The whole trip took her 7 hours. How many hours did Anika travel at each speed?

a) 3 hours at 43 km/h, 4 hours at 81 km/h
b) 4 hours at 43 km/h, 3 hours at 81 km/h
c) 5 hours at 43 km/h, 2 hours at 81 km/h
d) 2 hours at 43 km/h, 5 hours at 81 km/h

Answer 1

Anika drove for approximately 3 hours at 43 km/h and 4 hours at 81 km/h to cover the 448 km distance to her mother's place.

Step-by-step explanation:

Anika traveled 448 km to visit her mother, with part of the journey at 43 km/h and the remainder at 81 km/h, taking a total of 7 hours. To solve for the time spent at each speed, we can use the formula for distance:

Distance = Speed × Time.

Let the time traveled at 43 km/h be x hours. Accordingly, the time traveled at 81 km/h would be 7 - x hours, as the total time is 7 hours.

The total distance traveled is the sum of the distances traveled at each speed:

43 km/h × x hours + 81 km/h × (7 - x) hours = 448 km.

Solving for x gives us two equations:

43x (the distance covered at 43 km/h) + 81(7 - x) (the distance covered at 81 km/h) = 448

Expanding the equation:

43x + 567 - 81x = 448

Combining like terms yields:

-38x + 567 = 448.

Subtracting 567 from both sides:

-38x = -119

Dividing both sides by -38:

x = 3.1316, approximately 3 hours.

Thus, Anika drove 3 hours at 43 km/h and 4 hours at 81 km/h.