Mr. Bailey mowed his yard in 90 minutes. His son Roy mows the yard in 75 minutes. How long will it take them if they work together (using 2 lawn mowers)?
How to set up an equation? Thank you.
B does 1/90 yards/min
R does 1/75 yards/min
B+R together do (1/90 + 1/75)yards per minute
1/90 + 1/75 = .0244 yards/min
1/.0244 = 40.9 minutes/yard
Thank you so much!
To set up an equation for this problem, let's first define some variables. Let's call the time it takes Mr. Bailey to mow the yard alone "B" (in minutes), and the time it takes Roy to mow the yard alone "R" (in minutes).
Given that Mr. Bailey mowed the yard in 90 minutes (B = 90) and Roy can mow the yard in 75 minutes (R = 75), we need to find the time it takes them to mow the yard together, denoted as "T" (in minutes).
Since we are considering them working together, we can assume that the rates at which they mow the yard add up. So, the equation can be set up as follows:
1/B + 1/R = 1/T
Substituting the given values, we get:
1/90 + 1/75 = 1/T
To solve for T (the time it takes them working together), we need to find the least common multiple (LCM) of 90 and 75, as the LCM will be the denominator for the equation. The LCM of 90 and 75 is 450. So, the equation becomes:
(450/90) + (450/75) = 1/T
Simplifying further:
5/2 + 6/1 = 1/T
10/2 + 12/2 = 1/T
22/2 = 1/T
11 = 1/T
To find T, we can take the reciprocal of both sides of the equation:
1/11 = T
Therefore, it will take Mr. Bailey and Roy working together 1/11 of an hour or approximately 5 minutes and 27 seconds to mow the yard using 2 lawn mowers.