Problem solving using rational expressions

Question

A hurricane strikes a rural area without food or water. Three crews arrive. One can dispense food in 10 hrs a second in 15hrs and a third in 20hrs. How long will it take all three crews working together to dispense supplies. Okay to round one decimal place. solve using 6 steps if you can please 1. analyze 2. assign 3. form 4. solve 5. state 6. check

Answer 1

1/10 + 1/15 + 1/20 + 1/T where T = hours working all together

multiply by 60T

6T + 4T + 3T = 60

13T = 60

T = 60/13 = about 4.615 hours =4.6 hours rounded off to one decimal

Let's say they all averaged 15 hours, which they do, or assume they all could do it alone in 15 hours. 3 people would then do it in exactly 15/3 = 5 hours

the closer they are to equality, the closer they will be to 5 hours. 4.6 is close

10 and 20 are close to 15.

the 1st does 1/10 of the job in 1 hour, the 2nd does 1/15 of the job in 1 hour

the 3rd does 1/20 of the job in one hour.

Add them all up and that's the fraction they all do together in 1 hour

put them over a common denominator: 60T

1/10 + 1/15 + 1/20 = 1/T

6T/60T + 4T/60T + 3T/60T = 60/60T

add them up

(6T+4T+3T)/60T = 60/60T

13T/60T = 60/60T

if the denominators are the same on left and right sides, then the numerators are equal

13T =60. divide by 13

T =60/13 = about 4.5 hours working together.