Question

Anthony leaves Kingstown at $\text{2:00\hspace{0.33em}P.M.}$and drives to Queensville, $\text{160mi}$distant at $\text{45\hspace{0.33em}mi}/\text{h}$. At $\text{2:15\hspace{0.33em}P.M.}$Helen leaves Queensville and drives to Kingstown at $\text{40\hspace{0.33em}mi}/\text{h}$. At what time do they pass each other on the road?

Short answer

The time they pass each other on the road is$1\frac{3}{4}\text{hr}$ after$2:15\text{P.M}$ or at $4:00\text{P.M}$.

Step-by-step solution

Step 1. Write the given information.

The time at which A leaves Kingstown is $2:00\text{PM}$.

The speed of A is $45\text{\hspace{0.33em}mi}/\text{hr}$.

The time at which H leaves Queensville is $2:15\text{PM}$.

The speed of H is $40\text{\hspace{0.33em}mi}/\text{hr}$

Step 2. Form the system of equations.

The expression for speed is given by,

$\text{Distance}=\text{Speed}\times \text{Time}\mathrm{...}\left(1\right)$

The difference between time of A and H is,

$\begin{array}{c}\text{TimeDifference}=2:15-2:00\\ =15\text{min}\\ =\frac{1}{4}\text{hr}\end{array}$

Substitute$\frac{1}{4}$ for Time and$45$ for speed to calculate the distance covered by A.

$\begin{array}{c}{\text{Distance}}_A=45\times \frac{1}{4}\\ =11.25\text{mi}\end{array}$

Step 3. Calculate the point of meet.

The remaining distance is calculated as,

$\begin{array}{c}\text{RemainingDistance}=160-11.25\\ =148.75\text{mi}\end{array}$

The time when they pass each other is calculated as,

$\text{Timeofmeeting}=\frac{\text{RemainingDistance}}{\left(\text{Speedof}A+\text{Speedof}H\right)}$

Substitute the values in the above expression.

$\begin{array}{c}\text{Timeofmeeting}=\frac{\text{148.75}}{\left(40+45\right)}\\ =\frac{148.75}{85}\\ =1.75\text{h}\\ =1\frac{3}{4}\text{hr}\end{array}$

Thus, the time they pass each other on the road is$1\frac{3}{4}\text{hr}$ after$2:15\text{P.M}$ or at $4:00\text{P.M}$.