let

x = minutes that Jonah needs to complete the chores thus he works with a rate of 1/x chores per minute

y = minutes that Caleb needs to complete the chores thus he works with a rate of 1/y chores per minute

it takes Jonah 36 min longer than his brother to complete the chores

x = y + 36

the together rate of Jonah and Caleb 1/80 chores per minute

1/x + 1/y = 1/80

plug x = y + 36 into the last equation 1/x + 1/y = 1/80

1/(y + 36) + 1/y = 1/80

by solving we find and consider the positive roots (the can not be negative)

y = 144 min

click here to see the step by step solution of the equation

Caleb needs 144 minutes to complete the chores alone.