if a horse and a half can eat a bail of hey and a half in a day and a half, how long will 10 horses take to eat 10 bales of hay

Question

This is a question that grandma asked my to teenagers and they are lost!!

Answer 1

What i think you're saying is 1½ horses can eat 1½ bales of hay in 1½ days. So let's build a proportion from that.

 

If it takes 1½ horses to eat that amount in that time, then how much could just one horse eat? We'd have to reduce the amount by 1/1.5. That means that one horse can only eat 1 bale of hay in 1½ days. So how much can one horse eat in one day? Well, we'll need to reduce the amount eaten by 1/1.5 again.

 

That means that one horse can eat 2/3 bales of hay per day.

 

Using that, how much can ten horses eat per day? Well, there are ten of them, and if each of them eats 2/3 bales per day, then the group of them eat 20/3 bales per day. So how long does it take a group of horses eating 20/3rds bales of hay per day to eat 10 bales? The answer is however many times 20/3 goes into 10, so 10/(20/3)=30/20 = 1½. It takes ten horses a day and a half to eat 10 bales of hay.