Math
posted by Sara on .
1) Matt traveled the first leg of his trip for 1350 miles on a large jet. He then traveled an additional 600 miles on a private plane to reach his destination. If the speed of the jet was three times the speed of the plane and the total time in the air was 6 hours determine the speed of each aircraft.
2) Matt and Sara mow lawns together. When Matt mows the lawn for Mr. Smith it takes 100 minutes. When matt and Sara work together to mow the lawn for Smith they get the job done in 40 minutes. How long will it take Sara to mow Smith's lawn by herself?

speed of private plane  x mph
speed of jet > 3x mph
time for 1st leg of trip = 1350/x
time for 2nd leg of trip = 600/(3x) = 200/x
so 1350/x + 200/x = 6
1550/x=6
6x = 1550
x = 258.333..
private plane went 258.33 mph, jet went 775 mph 
Matt's rate = lawn/100
Sara's rate = lawn/x , where x is Sara's time if she works alone
combined rate = lawn/100 + lawn/x
= (xlawn + 100lawn)/(100x)
= lawn*(x+100)/(100x)
then lawn*(x+100)/(100x) = lawn/40
(x+100)/(100x) = 1/40
crossmultiply
100x = 40x + 4000
60x = 4000
x = 66.666. or 66 2/3 minutes