Question 118148
let x=speed of Jaguar, y=speed of Mercedes


Translate the first sentence "A jaguar traveled 1.2 times as fast as a Mercedes" to get the equation {{{x=2y}}}. Now translate the second sentence "the difference in their speeds was 24km /h" to get the equation {{{x-y=24}}}




Start with the given system

{{{x-y=24}}}
{{{x=2y}}}




{{{(2y)-y=24}}}  Plug in {{{x=2y}}} into the first equation. In other words, replace each {{{x}}} with {{{2y}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{y=24}}} Combine like terms on the left side





Now that we know that {{{y=24}}}, we can plug this into {{{x=2y}}} to find {{{x}}}




{{{x=2(24)}}} Substitute {{{24}}} for each {{{y}}}



{{{x=48}}} Simplify



So our answer is {{{x=48}}} and {{{y=24}}}




So the speed of the Jaguar is 48 km/h and the speed of the Mercedes is 24 km/h