Question

A car (Car A) leaves a gas station and travels along a straight road 200 miles long at a uniform speed of 40 miles per hour. A second car (Car B) leaves the station 1/2 hour later and travels along the same road at 55 miles per hour. At what time will Car B overtake Car A?

Answer 1

Answer:

$\boxed{\text{1 h 50 min}}$

Step-by-step explanation:

Let t = hours spent by Car A and

t - ½ = hours spent by Car B

The important point is that both cars have travelled the same distance by the time they meet.

$\text{Distance} & = & \text{rate} \times \text{ time}$

$\begin{array}{rcl}40t & = & 55(t - 0.5)\\40t & = & 55t - 27.5\\-15t & = & -27.5\\t & = & \frac{11}{6}\text{ h}\\& = & 1\frac{5}{6}\text{ h}\\& = & \textbf{1 h 50 min}\\\end{array}\\\text{Car B will overtake Car A in \boxed{\textbf{1 h 50 min}} }$

Check:

$\begin{array}{rcl}40\times \frac{11}{6} & = & 55(\frac{11}{6} - \dfrac{1}{2})\\\frac{440}{6} & = & 55 \left(\frac{8}{6}\right)\\\\\frac{440}{6} & = & \frac{440}{6}\\\end{array}$

OK.