If anyone can show me how to do these, it would be great.

1)Twin brothers, Andy and Brian, can mow their grandparents lawn together in 90 minutes. Brian can mow the lawn by himself in 19 minutes more than it would take Andy. How long would it take to each mow the lawn?

2) A boat travels 10 km upsteam and 10 km back. The time for the roundtrip is 9 hours. The speed of the stream is 5 km/h. What is the speed of the boat in still water?

Relevance

1) Andy alone takes x minutes

Brian alone takes ( x+19) minutes

Andy alone in 1 minute does 1 /x of the job

Brian alone in 1 minute does 1/ ( x+19) of the job

Together in 1 minute they do ( 1/x + 1/ ( x+19) ) of the job

Since together they take 90 minutes , in 1 minute they do 1/90 of the job

1/x + 1/ ( x+19) = 1/90

MULTIPLY BOTH SIDES BY 90x( x+19)

90 ( x+19) + 90x = x ( x+19)

90x + 1710 +90x = x^2 +19x

x^2 - 161x - 1710 = 0

x^2 + 10x - 171x -1710 = 0

x ( x+10) -171 ( x + 10) = 0

( x-171) ( x+10) = 0

Rejecting the negative value

x = 171

ANSWER Andy alone 171 minutes Brian = 190 minutes

CHECK

1/171 + 1/190 = 361/32490 = 1/90

2) Let speed of boat in still waters be x km/ hour

10/ (x+5) + 10/ ( x-5) = 9

10 ( x-5) + 10( x+5) = 9 ( x+5) ( x-5)

20x = 9x^2 - 225

9x^2 -20x - 225 = 0

9x^2 - 20x = 225

DIVIDE BY 9

x^2 - 20/9x = 225/9

x^2 -20/9x + 100/81 = 100/81 +225/9 = 2125/81

( x - 10/9) ^2 = 2125/81

x = 1/9 ( 10 + \/2125 ) OR 1/9 ( 10 - \/2125 )

Rejecting the negative value

x = 6.233 km/ hour ANSWER

CHECK

10/ (6.233+5) = 10/11.233 = 0.89hours

10/ ( 6.233-5) = 10/1.233 = 8.11 hours