Question

Twin brothers, Billy and Bobby, can mow their grandparent’s lawn together in 63 minutes. Billy could mow the lawn by himself in 25 minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by himself? I’ve tried multiple problems like this but I keep getting them wrong, please help.

Answer 1

Answer:

140 minutes

Step-by-step explanation:

this problem focuses on the combined work rate

both can finish the work under 63 minute

let bobby mow the lawn in x minute

Billy will then mow the lawn in x-25 minutes

Let the completed job = 1 (a mowed lawn)

we can now apply the combined work formula for the two boys as

$\frac{63}{x}+\frac{63}{x-25}=1$

multiplying through by x(x-25 )we have

$63(x-25)+63x= x(x-25)$

open bracket we have

$63x-1575+63x= x^2-25x$

rearranging and collecting like terms we have

$0=x^2-25x-63x-63x+1575 \\\\0=x^2-151x+1575 \\\\x^2-151x+1575=0$

we can now use the quadractic formula

$x=\frac{-b\frac{+}{} \sqrt{b^2-4ac} }{2a}$

 

a= 1

b= -151

c= 1575

$x=\frac{-(-151)\frac{+}{} \sqrt{151^2-4*1*1575} }{2*1}$

$x=\frac{-(-151)\frac{+}{} \sqrt{22801-6300} }{2} \\\\x=\frac{-(-151)\frac{+}{} \sqrt{16501} }{2} \\\\x=\frac{-(-151)\frac{+}{} 128.45}{2}$

$x=\frac{-(-151)+128.45}{2} \\\\\x=\frac{279.45}{2} \\\\x=139.72 \\\\\\x=\frac{-(-151)-128.45}{2}\\\\x=\frac{151-128.45}{2}\\\\x=\frac{22.55}{2}\\\\x=11.27$

the first answer x= 139.72 approximately 140 minutes mins is correct for  Bobby's time

let us check

$\frac{63}{140}+\frac{63}{140-25}=1\\\\\\0.45+\frac{63}{115} =1\\\\0.45+0.5478=1\\0.997 =1$

we can see that the solution approximates to 1