Can anybody get these two word problems? There simpler but for some reason I cant get it. Thank you!

Question

1) Candy and Tim share a paper route. It takes Candy 80 min to deliver all the papers, and it takes Tim 70 min. How long does it take the two when they work together?

 

 

2) Stan and Hilda can mow the lawn in 60 min if they work together. If Hilda works twice as fast as Stan, how long does it take Stan to mow the lawn alone?

Answer 1

Hi, Hero.

 

There's a pretty simple formula that you can use to find the solution to your problems.

 

Let x = the time needed for Candy and Tim to work together

Let the completed job (the whole paper route) = 1

 

Candy and Tim will each do a fraction of the work, and their fractions will add up to 1.

 

(x/80) + (x/70) = 1

 

Find the common denominator for the two fractions, in this case 560. You'll have to multiply the numbers in the first fraction by 7 to change it from x/80 to 7x/560, and multiply the numbers in the second fraction by 8 to get 8x/560. So now your equation should look like this:

 

(7x/560) + (8x/560) = 1

 

Now that you have the fractions sharing a common denominator, you can add them up. 7x plus 8x equals...

 

15x/560 = 1

 

Multiply each side of the equation to clear the denominators.

 

15x = 560

 

Divide each side by 15 to find x, and then you'll have the number of minutes it takes for Candy and Tim to complete their paper route together.

 

x = 37.333333... or 37 minutes and 20 seconds.

 

For your second question you can first find the amount of work Stan does in one hour by figuring that since Hilda works twice as fast and does twice as much work, that she mows two thirds of the lawn while Stan mows one third. If in 60 minutes Stan mows one third of the lawn, it will take him three times as long to mow three thirds or all of the lawn. Keep simplifying the equation until you solve for y.

 

60 = y(1/3)    

 

y times 1/3 is the same as y/3, just like 1 times 1/3 is the same as 1/3.

 

60 = y/3

 

Multiply each side by 3.

 

180 = y

 

So it will take Stan 180 minutes or 3 hours to mow the lawn by himself. If Hilda works twice as fast, how long would it take her to mow the same lawn by herself?

 

 

Answer 2

1) Candy does 1/80 of the job per minute and Tim does 1/70 of the job per minute.

    x=# of minutes it takes for them to do the job together

    (1/80)(x)+(1/70)(x)=1 (job finished)

    multiply both sides by the lcm of 70 and 80 which is 560

   (560)(x/80)+(560)(x/70)=560

   7x+8x=560

   15x=560

   x=560/15=37 1/3 minutes

 

2) (1/x)(60)+(1/2x)(60)=1

    (60/x)+(60/2x)=1

    (60/x)+(30/x)=1

    (90/x)=1

    90=x

    x=90 minutes for Hilda

    2x=180 minutes for Stan