It takes Harry 20 minutes longer to tie his shoes than Lloyd. Working together, they can tie Harry's shoes in 45 minutes. How long does it take Harry to tie his shoes working alone?

1 Answer
seol
Sep 11, 2017

Harry takes 32.5 minutes to tie his shoes. Lloyd takes 12.5 minutes to tie Harry's shoes.

Explanation:

Harry = #h#, Lloyd = #k#

"It takes Harry 20 minutes longer to tie his shoes than Lloyd." #h=20+k#
"Working together (Harry and Lloyd), they can tie Harry's shoes in 45 minutes." #h+k=45#

Since you have an equation for one of the variables, #\color(steelblue)(h=20+k)#, you can replace it into the other equation with two variables, #\color(steelblue)(h)+k=45#

#\therefore(\color(steelblue)(20+k))+k=45#
#20+2k=45# add all variables
#2k=45-20# isolate variable term
#2k=25# simplify
#k=25/2# divide
#k=12.5# minutes.

Now plug in Lloyd's time, #\color(indianred)(k=12.5)#, into the equation for Harry's time, #h=20+\color(indianred)(k)#.

#\thereforeh=20+(\color(indianred)(12.5))#
#h=32.5# minutes.

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