Excluding breaks, it took Chun a total of 10 hours to bike to a cousin’s home and return. On the way, Chun biked alone and averaged 15 mph. On the way back, with his cousin, he averaged 10 mph. How many miles was it to his cousin’s home?

the distance to his cousin's home is 60 miles

Step-by-step explanation:

Let t represent the time that it took Chun to bike to cousin’s home.

Excluding breaks, it took Chun a total of 10 hours to bike to a cousin’s home and return. This means that the time it took Chun and his cousin to return is 10 - t

Distance = speed × time

On the way, Chun biked alone and averaged 15 mph. This means that the distance that Chun covered in

t hours is 15t

On the way back, with his cousin, he averaged 10 mph. This means that the distance that they covered on their way back is

10(10 - t)

Since the distance remains the same, it means that

15t = 10(10 - t) = 100 - 10t

15t + 10t = 100

25t = 100

t = 100/25

t = 4

Therefore, the number of miles to his cousin’s home is

15t = 15 × 4 = 60 miles