misfortune in madrid
1.
If 6 workers can harvest a field in 18 hours, how many workers would it have taken to do it in 3 hours?
Solution:
Let x be the number of workers it would have taken.
(6 workers)(18hours)
=(3 hours) x
(3 hours)x
108 worker-hours
=3x hours
3x hours
36 workers
=x
x
2.
If 8 workers can plant a garden in 6 hours, how many workers would it have taken to do it in 4 hours?
Solutions:
Let x be the number of workers it would have taken.
(8 hours) (6 hours) = (4 hours) 48 worker-hours=4x hours 12 workers=x
3.One pipe can empty a tank 2.5 times faster than another pipe. Starting with a full tank, if both pipes are turned on, it takes 7.5 hours to empty the tank. How long does it take the faster pipe working alone to empty a full tank?
Solutions:
Let f = number of hours it takes the faster pipe and 2.5f = number of it takes the slower pipe 1 tank +1 tank = 1 tank F 2.5f 7.5 hours
Solve for f to get f= 10.5
Working alone,the faster pipe takes f.
Answer: f:10.5 hours
Example 1:
Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?
Solution:
Step 1: Assign variables:
Let x = time taken by Peter
Step 2: Use the formula:
Step 3: Solve the equation
Multiply both sides with 30x
Answer: The time taken for Peter to paint the fence alone is hours.
Example 1:
Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?
Solution:
Step 1: Assign variables:
Let x = time to mow lawn together
Step 2: Use the formula:
Step 3: Solve the equation
The LCM of 40 and 60 is 120 Multiply both sides with 120
Answer: The time taken for both of them to mow the lawn together is 24 minutes.
If 6 workers can harvest a field in 18 hours, how many workers would it have taken to do it in 3 hours?
Solution:
Let x be the number of workers it would have taken.
(6 workers)(18hours)
=(3 hours) x
(3 hours)x
108 worker-hours
=3x hours
3x hours
36 workers
=x
x
2.
If 8 workers can plant a garden in 6 hours, how many workers would it have taken to do it in 4 hours?
Solutions:
Let x be the number of workers it would have taken.
(8 hours) (6 hours) = (4 hours) 48 worker-hours=4x hours 12 workers=x
3.One pipe can empty a tank 2.5 times faster than another pipe. Starting with a full tank, if both pipes are turned on, it takes 7.5 hours to empty the tank. How long does it take the faster pipe working alone to empty a full tank?
Solutions:
Let f = number of hours it takes the faster pipe and 2.5f = number of it takes the slower pipe 1 tank +1 tank = 1 tank F 2.5f 7.5 hours
Solve for f to get f= 10.5
Working alone,the faster pipe takes f.
Answer: f:10.5 hours
Example 1:
Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?
Solution:
Step 1: Assign variables:
Let x = time taken by Peter
Step 2: Use the formula:
Step 3: Solve the equation
Multiply both sides with 30x
Answer: The time taken for Peter to paint the fence alone is hours.
Example 1:
Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?
Solution:
Step 1: Assign variables:
Let x = time to mow lawn together
Step 2: Use the formula:
Step 3: Solve the equation
The LCM of 40 and 60 is 120 Multiply both sides with 120
Answer: The time taken for both of them to mow the lawn together is 24 minutes.