Question

Chloe started biking to the park at 10 mph. After getting a flat tire, she walked the rest of the way at 2 mph. If the total trip took 11 hours and covered 62 miles, how long did Chloe travel at each speed?

a. Biked for 5 hours, walked for 6 hours
b. Biked for 4 hours, walked for 7 hours
c. Biked for 6 hours, walked for 5 hours
d. Biked for 7 hours, walked for 4 hours

Answer 1

The correct answer is option 'a', where Chloe biked for 5 hours and walked for 6 hours, totaling 62 miles in 11 hours.

Step-by-step explanation:

The correct answer is option 'a'. Chloe biked for 5 hours and walked for 6 hours. To solve the problem, we can set up two equations based on the distances traveled at each speed and the total time. Let x be the number of hours Chloe biked and y the number of hours she walked. We have two relationships:

1. 10 mph × x + 2 mph × y = 62 miles (Total distance equation)
2. x + y = 11 hours (Total time equation)

From the second equation, we can express y as:

y = 11 - x (Rearranged total time equation)

Substitute y in the first equation and solve for x:

10x + 2(11 - x) = 62

10x + 22 - 2x = 62

8x + 22 = 62

8x = 62 - 22

8x = 40

x = 40 / 8

x = 5

Therefore, Chloe biked for 5 hours at 10 mph. To find y, substitute x back into the rearranged total time equation:

y = 11 - 5

y = 6

Chloe walked for 6 hours at 2 mph. This solution aligns with the distances and times that add up correctly for a total trip of 62 miles in 11 hours.