Question

The grounds crew needs to mow the football field before their next game. Mr. Comb can mow the field in 5 hours, and Mr. Ramset can mow the same field in 4.5 hours. If they worked together, how long would it take for both of them to mow the field if they worked together? Round your answer to the nearest minute.

Answer 1

2 hours and 22 minutes

Explanation:

Rate x Time = jobs

Mr. Comb's rate is 1 field in 5 hours or 1/5.

Mr. Ramset's rate is 1 fiend in 4.5 hours.

If we take the time and rate that it takes Mr. Comb's to mow one field and add it to the time and rate that it takes Mr. Ramset's to move one field we can find out how long it takes them to mow one field together

RT + RT = 1 (job)

1/5T + 1/4.5T = 1 We need a common denominator. I just multiplied 5 x 4.5 for get 22.5 Rewrite 1/5 and 1/4.5 with a common denominator or 22.5 we get the equivalent fractions that we can add together.

4.5/ 22.5T + 5/22.5T = 1 Add the fractions together

9.5/22.5T = 1 We want to solve for T, so we will multiply both sides of the equation by 22.5/9.5

9.5/22.5(22.5/9.5)T= 1 22.5/9.5

T = 22.5/9.5 When I divide these, I get 2 35/95 hours. I need to change the fraction part of an hour to minutes. I will use the unit multiplies 60 minutes/ 1 hour.

35hours/95 (60 minutes/1 Hour) = 22.10526331579. I need to round this to the nearest minutes which will be 22 minutes.