Question

Nathaniel left Los Angeles on the interstate, driving east towards Albuquerque at a speed of 48 miles per hour. Half an hour later, Mikaela left Los Angeles driving in the same direction at a speed of 72 miles per hour. If they both drove continuously at their given speeds, how long will it take Mikaela to catch up to Nathaniel?

Answer 1

Step 1

Nathaniel

Start time = t

Speed = 48

$\text{Distance = 48t}$

Step 2

Mikaela

$\begin{gathered} \text{Start time = t - 0.5} \\ \text{Speed = 72} \\ \text{Distance = 72(t - 0.5)} \end{gathered}$

Step 3

Equate the two distance

$\begin{gathered} 48t\text{ = 72(t - 0.5)} \\ 48t\text{ = 72t - 36} \\ 36\text{ = 72t - 48 t} \\ \text{36 = 24t} \\ \text{t = }\frac{36}{24} \\ \text{t = }\frac{3}{2}\text{ = 1}\frac{1}{2}\text{ hours} \end{gathered}$

Final answer

$It\text{ take( 1}\frac{1}{2}-\frac{1}{2})=1\text{ hours to catch up}$

Answer: 1 hour