Getting the Job Done—Work 05:30 minutes

Video Transcript

Transcript Getting the Job Done—Work

Once upon a time... There lived two sisters, Margarete and Matilda. Margarete is cheerful and always works quickly. Matilda, not so much. The sisters are on their way to meet the magical fairy Holly. On their way, they will encounter challenges. To see how they complete the challenges ahead, we need to understand how they get the job done using work rates. On their way, they come across two trees in trouble. Their branches are heavy with apples and the trees need a rest! They ask the sisters to shake some apples from their branches. Each sister goes to a tree and starts shaking. "Happy to help, Margarete shakes off apples from her tree at a rate of 240 apples per 30 seconds." Meanwhile, Matilda shakes off apples from her tree at a rate of only 8 apples per 2 seconds. These are Margarete and Matilda's work rates, or rates at which work is done in a certain amount of time. In order to compare Margarete and Matilda's work rates, we must rewrite them so that both work rates have the same denominator. We can do this by converting each work rate to their unit work rate, or how many apples shaken off per one second. Dividing the numerator and denominator by 30, we see that Margarete shakes off 8 apples per second. Nice work, Margarete! Dividing the numerator and denominator of Matilda's work rate by 2 gives Matilda a unit work rate of 4 apples per second. Nice effort, Matilda. Now we can compare which sister shook the most apples per second. Comparing Margarete's and Matilda's work rates, we see that Margarete shook twice as many apples per second. Margarete is definitely the better apple shaker! Is anyone surprised? The sisters continue through the woods and smell bread baking in two stone ovens. Uh oh, the bread loaves in the ovens are calling for help. The sisters rush to remove the baking bread. If they don't get taken out quickly, they'll burn! Margarete takes out 180 loaves in 15 seconds. Impressive! Matilda takes out 200 loaves in 40 seconds. Hey, that's more loaves than Margarete! Simplifying the fraction gives Margarete a unit work rate of 12 loaves per second. Simplifying Matilda's work rate, though, gives a measly 5 loaves per second. What a slowpoke. Comparing the unit work rates side by side, we see that even though Matilda removed a little more bread, it took her a lot more time. So Margarete's work rate is actually faster. Better luck next time, Matilda. The sisters trudge on and finaly come to meet the sweet, magical fairy Holly. Holly has a pile of feather pillows. She needs the sisters to shake out as many feathers from the pillows as possible, so that she can make it snow! To complete this last task, the sisters will have to work together. Margarete shakes out 1675 feathers in 25 seconds. Matilda's arms are tired from all the bread and the apples! She shakes out just 260 feathers in 20 seconds. Margarete's unit work rate is 67 feathers per second. While Matilda's is only 13 feathers per second! But this time, the sisters aren't competing, they're working together. What is the sisters' combined work rate? We can figure this out by adding the sisters' unit work rates together, as they are fractions with the same denominator. 67 feathers per second plus 13 feathers per second is 80 feathers per second in total. Sadly, the magical fairy Holly says that the sisters did not work quickly enough make it snow. That's it! Matilda has had it with all this work! Oof! This should do the trick! As the snow falls, Matilda hears trumpets and cheers. Huh? It's just Matilda's phone alarm, waking her up for school. Wait a minute school's canceled! It's a snow day! The sisters did make it snow after all!