The average speed of Car 1 = 45 mph.The average speed of Car 2 = 65 mph.Time elapsed between the start of Car 1 and start of Car 2 = 18 minutes.How long before Car 2 overtakes Car 1? ____ hour.
Accepted Solution
A:
Answer:[tex]\boxed{\text{0.675 h}}[/tex]Step-by-step explanation:18 min = 0.3 h
Car 1 started 0.3 h before Car 2.
Let t = time of Car 2. Then
t + 0.3 = time of Car 1
Distance = speed × time, and both cars travel the same distance. Then
[tex]\begin{array}{rcl}45(t + 0.3) & = & 65t\\45t + 13.5 & = & 65t\\20t & = & 13.5\\t & = & \textbf{0.675 h}\\\end{array}\\\text{Car will overtake Car 1 in } \boxed{\textbf{0.675 h}}[/tex]
Check:
[tex]\begin{array}{rcl}45(0.675 + 0.3) & = & 65 \times 0.675\\45 \times 0.975 & = & 43.875\\43.875 & = & 43.875\\\end{array}[/tex]OK.