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A man travels from Town A to Town B at an average speed of $4\,\text{km/h}$ and from Town B to Town A at an average speed of $6\,\text{km/h}$ .If he takes $45$ minutes to complete the entire journey.Find the total distance travelled

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Rate of travel: word problems

Full solution

Q. A man travels from Town A to Town B at an average speed of

4\,\text{km/h}

and from Town B to Town A at an average speed of

6\,\text{km/h}

.If he takes

45

minutes to complete the entire journey.Find the total distance travelled

Convert to hours: First, convert the total travel time from minutes to hours because the speeds are given in km/h. $\newline$ $45$ minutes = $\frac{45}{60}$ hours = $0.75$ hours.
Distance and time: Let the distance from Town A to Town B be $x$ km. The time taken to travel from Town A to Town B at $4$ km/h is $\frac{x}{4}$ hours. The time taken to travel from Town B to Town A at $6$ km/h is $\frac{x}{6}$ hours.
Total time calculation: The total time for the journey is the sum of the times for each leg. $\newline$ Total time = Time from A to B + Time from B to A $\newline$ $0.75$ hours = $\frac{x}{4}$ + $\frac{x}{6}$
Combine terms: To solve for $x$ , find a common denominator and combine the terms. $(3x + 2x) / 12 = 0.75$ $5x / 12 = 0.75$
Isolate $x$ : Multiply both sides by $12$ to isolate $5x$ . $5x = 0.75 \times 12$ $5x = 9$
Solve for x: Divide both sides by $5$ to solve for x. $\newline$ $x = \frac{9}{5}$ $\newline$ $x = 1.8$ km
Total distance calculation: The total distance traveled is twice the distance from Town A to Town B because the man travels to Town B and back to Town A. $\newline$ Total distance $= 2 \times x$ $\newline$ Total distance $= 2 \times 1.8 \, \text{km}$ $\newline$ Total distance $= 3.6 \, \text{km}$

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