Problema Solution
Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 6 hours working together find how long to the nearest tenth of an hour it takes for William to cut the lawn alone.
Answer provided by our tutors
let
s = the hours Shelly needs to cut the lawn alone, thus her rate is 1/s lawns per hour, s>0
w = the hours William needs to cut the lawn alone, thus her rate is 1/w lawns per hour,w>0
they can cut the lawn in 6 hours working together thus their together rate is 1/6 lawns per hour
1/s + 1/w = 1/6
Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower:
s = w - 5
since s >0 we have w - 5 > 0 or w > 5
plug s = w - 5 into 1/s + 1/w = 1/6
1/(w - 5) + 1/w = 1/6
by solving we find
w = 15 hours
click here to see the step by step solution of the equation
William can cut the lawn alone in 15 hours.