A town has two trucks to collect garbage. When both truck are in use, they take 6 hours to collect all the garbage. When only the small truck is in use it takes 24 hours to collect the garbage how long would it take to collect the garbage if only the large truck is in service?

8 hours

Step-by-step explanation:

In this case, the speed would be given by the garbage collection / hour, therefore the two together, that is to say from the sum of both, would be 1/6 the speed and for the small truck it would be 1/24

So to calculate the speed of the big truck it would be:

1/24 + 1 / x = 1/6

1 / x = 1/6 - 1/24

1 / x = 0.125

x = 1 / 0.125

x = 8

Which means that only the big truck would take only 8 hours