math word probelms

Question

twin brother, billy and bobby, can mow their grandparents lawn together in 71 minutes. Billy could now the lawn by himself in 30 minutes less time that it would take bobby. how long would it take bobby to mow the lawn by himself?

Answer 1

Let x = number of minutes that it takes Bobby to mow the lawn by                  himself

 

x - 30 = number of minutes that it takes Billy to mow the lawn by                      himself

 

Each minute, Bobby mows 1/x of the lawn (for example, if it takes him 38 minutes to mow the lawn, he mows 1/38th of the lawn each minute).  Similarly, each minute Billy mows 1/(x-30) of the lawn.

 

Portion done by Bobby per minute + Portion done by Billy per minute = Portion done by both of them per minute

 

So, 1/x + 1/(x - 30) = 1/71

 

Multiplying both sides by the LCD, 71x(x-30), we get:

 

71(x-30) + 71x = x(x-30)

 

x² - 30x = 142x - 2130

 

x² - 172x + 2130 = 0 

 

x = (172 ± √21064)/2 = 158.6 or 13.4

 

x can't be 13.4 because, in that case, x - 30 would be negative

 

So, x = 158.6 minutes = 2hours 38.6 minutes