Question 696356
Try it this way:
Start a stopwatch when the faster one is
exactly 14 miles behind the slower one.
You will hit the stopwatch when the 
faster one has caught the slower one.
Call the time on the stopwatch {{{ t }}} ( in hours )
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Let {{{ d }}} = distance in miles that the slower one
travels until he is caught.
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Equation for slower one:
(1) {{{ d = 70t }}}
Equation for faster one:
(2) {{{ d + 14 = 98t }}}
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Substitute (1) into (2)
(2) {{{ 70t + 14 = 98t }}}
(2) {{{ 28t = 14 }}}
(2) {{{ t = .5 }}}
The faster one catches the slower one
in a half hour.
Looks like you did it right.