Algebra -- Rate question

Question

Curtis can unload a truckload of hay in 30 minutes, but it takes Ronnie 40 minutes to do the same. Working together, how many minutes will it take them to unload 35 truckloads of hay?

Answer 1

Curtis does 1/30 of the job in 1 minute

Ronnie does 1/40 of the job in 1 minute

x=# of minutes they do the job together

(1/30)x+(1/40)x=1  (job finished)

multiply both sides by 120, the LCD of 30 and 40

120(1/30)x+120(1/40)x=120(1)

4x+3x=120

7x=120

x=120/7

x=17 1/7 minutes together for 1 truck load

for 35 truckloads: (17 1/7)*35=(120/7)(35)=120*5=600 minutes or 10 hours

 

Answer 2

Algebra -- Rate question
Curtis can unload a truckload of hay in 30 minutes, but it takes Ronnie 40 minutes to do the same. Working together, how many minutes will it take them to unload 35 truckloads of hay?

 

=====================================

 

Let A be  the amount unloading work, and

     T  be the time of unloading (of one truckload)

 

What is new when 2 friends working together - they powers are added.

Let's find their powers (p1 and p2) and equalize their sum to needed power, i.e. P=A/T.

 

So,  p1=A/30   , and  p2=A/40

 

We know, p1+p2=A/T

 

From here, T=A/(p1+p2)

 

then,          T=A/(A/30+A/40)=120/7=17.1 (minutes)

IF both of them have equal "powers" - do the job during same time, say in 30 min, then together they surely

unload the truck 2 times faster - in 15 minutes, that is. But, because second worker is a bit slow ,they do the job in a "bit" slow way - in almost 17 minutes.

 

 

For the 35 truckloads, the needed time be 35 times greater T=35*17.1 (min)=598.5 (min)=9.97 (hours), almost 10hr.

 

Message if questions.

Good luck:)

 

Answer 3

If Curtis and Ronnie were both unloading the truck at, say, 30 min each, the number of minutes would be divided by two when working together. I would take this same approach.

 

You have two ratios: 1truckload/30minutes=35/x₁  and   1truckload/40 minutes= 35/x_2.

 

x₁=1050 minutes    

x₂=1400 minutes

 

The number in between 1050 and 1400 is 1225. Divide this by two and you have 612.5 minutes. (I believe this is right; I haven't done it in a while)