Question

Emily can rake her lawn in 5 hours. Andrew can rake the same lawn in 8 hours. Rounded to the nearest hour, how long will the job take if they work together?

Explain too, please. Thanks!

Answer 1

Emily and Andrew will take approximately 3 hours to complete the job if they work together.

Step-by-step explanation:

To determine how long it will take for Emily and Andrew to rake the lawn together, we can use the concept of work rates. Emily can rake the lawn in 5 hours, so her work rate is 1/5 of the lawn per hour. Andrew can rake the same lawn in 8 hours, so his work rate is 1/8 of the lawn per hour.

When they work together, their work rates are additive. So, the combined work rate will be 1/5 + 1/8 = 13/40 of the lawn per hour.

To find how long it will take for them to finish the job, we can invert the combined work rate:

Time = 1 / (13/40) = 40/13 ≈ 3 hours.

Answer 2

Emily can rake 1/5 of the lawn in an hr.
Andrew can rake 1/8 of the lawn in an hr.

Together, they rake 1 yardful. x represents time in hours.
(1/5)x+ (1/8)x= 1

Multiply all values by 40
8x+5x=40
13x=40
x= 40/13
x=3.0769...

Final answer: 3 hours