Algebraic word problem?

Question

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

answer: 37min 20sec

how would you go about figuring this out?

Answer 1

Let the total number of papers to be distributed be ‘ x ‘.

Candy delivers  x papers in 70 mins. Hence in one minute he delivers   ( x/70 ) papers.

Similarly Tim delivers  ( x/80 ) papers in one minute.

HENCE IN ONE MINUTE BOTH OF THEM working together  DELIVER =  ( x/70  

+  x/80 ).  =  15 x / 560  =  3 x / 112     PAPERS.

Now  3x/ 112  papers are delivered in one minute by them

therefore x papers  will need  =  ( x.1.112 / 3x )  =  37 minutes and  ( 1/3 ) 60 sec.

=>  37 min. 20 sec. …………………… Answer

Dr. PKT

Answer 2

Candy delivers 1/70 of the route in 1 minute

Tim delivers 1/80 of the route in a minute

Working together they deliver 1/70 +1 / 80 of the route per minute

1/70 + 1/80 = 15/560 = 3/112 route/minute

It will therefore take them 112/3 minutes/route = 37 and 1/3 min to deliver all the papers.

Answer 3

Looking at their speeds, you can say that Candy will deliver more papers in the same amount of time as Tim.  The ratio is 80/(80 + 70) = 53.33333% of the papers.  That means it will take her 53.33333% as long as her normal route => 70 min * 53.3333333% = 37.33333 or 37 minutes 20 seconds.  In that same amount of time, Tim delivers 46.66666% of the papers => 70/(70 + 80) => and together they have delivered 100% of the papers.

Answer 4

If they work together  C does 8/15ths of the round and T does 7/15ths.

So T finishes in 7/15 of 80 mins which is 37m.....

(or C finishes in 8/15 of 70 mins) whcih is the same thing.