Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the distance in 1.5 h. Car B traveled 15 mph faster than Car A. How fast did Car B travel? (The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.) Enter your answer for the box.

Accepted Solution

recall your d = rt, distance = rate * time

distance is the same "d" miles for each, if car A is going at a speed of "r", then B is going at a speed of "r+15"

[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{Car A}&d&r&2\\ \textit{Car B}&d&r+15&1.5 \end{array} \\\\\\ \begin{cases} \boxed{d}=2r\\ d=1.5(r+15)\\ ----------\\ \boxed{2r}=1.5(r+15) \end{cases} \\\\\\ 2r=1.5r+22.5\implies 0.5r=22.5\implies r=\cfrac{22.5}{0.5}\implies r=45[/tex]

how far is B going?  well, B's rate is r+15.