MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

Answer:[tex]\boxed{\text{1 h 50 min}}[/tex]Step-by-step explanation:Let t = hours spent by Car A and
t - Β½ = hours spent by Car B
The important point is that both cars have travelled the same distance by the time they meet.
[tex]\text{Distance} & = & \text{rate} \times \text{ time}[/tex][tex]\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 $\boxed{\textbf{1 h 50 min}}$}[/tex]Check:
[tex]\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}[/tex]OK.