Question 610912
Write a {{{ d = r*t }}} equation for each car
For the slower car:
(1) {{{ 300 = r[1]*t }}}
For the faster car:
(2) {{{ 450 = r[2]*t }}}
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given:
{{{ r[2] = r[1] + 25 }}}
Substitute this into (2)
(2) {{{ 450 = ( r[1] + 25 )*t }}}
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Now I have 2 equations and 2 unknowns, so it's solvable
(2) {{{ 450 = r[1]*t + 25t }}}
Substitute (1) into (2)
(2) {{{ 450 = 300 + 25t }}}
(2) {{{ 25t = 150 }}}
(2) {{{ t = 6 }}}
Plug this back into (2)
(2) {{{ 450 = r[2]*t }}}
(2) {{{ 450 = r[2]*6 }}}
(2) {{{ r[2] = 450/6 }}}
(2) {{{ r[2] = 75 }}}
The speed of the faster car is 75 mi/hr
check:
(1) {{{ 300 = r[1]*t }}}
(1) {{{ 300 = r[1]*6 }}}
(1) {{{ r[1] = 300/6 }}}
(1) {{{ r[1] = 50 }}}
This is 25 mi/hr less than the faster car, so
answer is correct
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The source of confusion is probably mixing up
the data for the 2 cars. make sure you keep it straight.