How do you do this math problem (rate)?

Question

A man can drain a pool in 4 hours, another can drain it in 3 hours. How long will it take if both men work together?

Also, can you help with this?
Bob can cut his lawn in 4 1/2 hours. His wife, Carla can cut in 4 hours and their son Tal can cut in 3 1/2hours
How long does it take for all 3 to cut the lawn?

Answer 1

The first man drains 1/4 of the pool in an hour and the second man drains 1/3 of the pool in an hour. Together they drain 1/4 + 1/3 = 7/12 of the pool in 1 hour. Invert that fraction to find out how long it takes them (in hours).

Answer 2

It depends how they're draining it. If they're using the pool's drain pipe, you'd have to know the capacity of the pipe, which you don't. If they're using separate equipment (pumps, or siphon hoses) and draining the water into a creek or onto the road where the capacity is of no importance, then the way to solve this is to add the inverses of the two times, then take the inverse of the sum. So 1/4 pool per hour + 1/3 pool per hour = 7/12 pool per hour. Invert 7/12 and you get 1 5/7 hours per pool, or 1 hour and 43 minutes (rounded to the nearest minute) to drain the pool. (5/7 x 60 = 43)

Answer 3

1)
Rate of the first man: R1=V/4
Rate of the second one: R2=V/3
Total Rate when they both work all together:
R=R1+R2= V/4 + V/3 = V(3/12 + 4/12) = V(7/12)
Time taken is: T=V/R = V/V(7/12) = 12/7 hr = 1hr 42 minutes and 51 seconds (after rounding the rest)

2)
Rate of Bob: R1 = W/4.5
Rate of Carla: R2= W/4
Rate of Tal: R3= W/3.5
Total Rate: R= R1 + R2 + R3 = W/4.5 + W/4 + W/3.5
By using a calculator:
= W(0.7579365)
==> T= W/W(0.7579365) = 1.31937 hr = 1 hr 19 minutes and 10 seconds (after rounding up)

Answer 4

rate x time = work

1/4+1/3 x Y = 1

3/12 + 4/12 x Y = 1
7/ 12 x Y = 1

just solve the equation for y and your set

Answer 5

3 hours

Answer 6

Subtract 4 and 3 together.
1 divide by 2
Answer .5 hours which would be 30 minutes