RATE PROBLEMS WITH FRACTIONS

Problem 1 :

Cara run 3 miles in 27  1/2 minutes. Melaine can run 6 miles in 53  1/3 minutes. Who can run faster ?

Solution :

To make a comparison, we have to convert both quantities into the same unit. Let us calculate the time taken to cover 1 mile for those persons separately.

Unit rate of Melaine is lesser, so she runs faster.

Problem 2 :

Emma drank 1/4 of a milk shake in 1/12 of a minute. How many minutes will it take her to drink a full milk shake.

Solution :

Time taken to drink 1/4 of milk shake = 1/12 minute

Let x be the minutes taken to drink it completely.

1/4 : 1/12 = 1 : x

So, time taken by Emma to drink the milk shake completely is 1/3 minutes.

Problem 3 :

Sophia used 1/3 an ounce of cheese to make 1/12 of pound of pizza dough. How many ounces of cheese are needed to make a pound of pizza dough ?

Solution :

Let x be the required quantity of cheese.

She needs 4 ounces.

Problem 4 :

Addison plays 1/2 of a song in 1/8 of a minute. How many minutes will he need to play full song ?

Solution :

Let x be the required number of minutes to play full song.

Number of minutes required = 4.

Problem 5 :

Joey fills 1/5 of a toffee box in 1/25 of a minute. How much time will he take to fill a toffee box ?

Solution :

Let x be the time taken to fill a toffee box.

Ratio between part of box : time taken

1/5 minutes is needed.

Problem 6 :

Clarie power walks 1/9 of a mile in 1/54 of an hour, compute the unit rates as complex fraction.

Solution :

Problem 7 :

Maya reads 1/8 of a newspaper in 1/20 of a minute. How many minutes does she need to read an entire paper?

Solution :

Let x be the number of minutes taken to read the entire paper.

Problem 8 :

Ellies used 1/6 of a liter of water to make 1/21 of a casserole. How many liters of does she need to make an entire casserole ?

Solution :

Let x be the required quantity of water. 

So, she needs 3  1/2  liter of water to make an entire casserole.

Problem 9 :

Stella writes 1/7 of a page in 1/15 of a minute. How many minutes does it take her to write a full page ?

Solution :

Let x be the minutes taken to write a full page.

So, he needs 7/15 minutes to write a full page.

Problem 10 :

Lillian eats 1/4 of pound of grapes in 1/17 of a minute. How many minutes will it take her to eat a full pound of grapes ?

Solution :

Let x be the minutes taken to eat.