Question 765115
This is a rate problem. Add their rate of covering
distance to get their rate working together.
a's rate is ( 1 distance covered ) / ( 3.5 hrs )
a and b together rate: ( 1 distance covered ) / ( 2.5 hrs )
Let {{{ t }}} = hrs for b alone to cover distance
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{{{ 1/3.5 + 1/t = 1/2.5 }}}
Multiply both sides by {{{ 2.5*3.5*t }}}
{{{ 2.5t + 2.5*3.5 = 3.5t }}}
{{{ 2.5t + 8.75 = 3.5t }}}
{{{ t = 8.75 }}}
b alone takes 8 hrs and 45 min to cover the same distance
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check:
{{{ 1/3.5 + 1/t = 1/2.5 }}}
{{{ 1/3.5 + 1/8.75 = 1/2.5 }}}
{{{ .2857 + .1143 = .4 }}}
{{{ .4 = .4 }}}
OK