Question 1039115
Start a stopwatch when the car leaves.
Let {{{ t }}} = the time on the stopwatch in
hrs when the car catches up with the truck
Let {{{ d }}} = the distance in km the car travels
until it catches up with the truck
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Equation for the car:
(1) {{{ d = 50t }}}
Equation for the truck:
(2) {{{ d - 5 = 40t }}}
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Substitute (1) into (2)
(2) {{{ 50t - 5 = 40t }}}
(2) {{{ 10t = 5 }}}
(2) {{{ t = 1/2 }}}
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The car catches up with the truck 1/2 after
the CAR leaves.This is an important point.
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If you wanted to know the time in hrs to catch the truck
after the truck leaves, you must add in the truck's time
to travel 5 km
{{{ 5 = 40t[1] }}}
{{{ t[1] = 1/8 }}}
{{{ t + t[1] = 4/8 + 1/8 = 5/8 }}}
The car catches the truck 5/8 hr after the TRUCK leaves.
This isn't what was wanted, so you don't care about it.