a man travels for 5 hours 15 minutes. if he covers the first half of the journey at 60 km/h and rest at 45 km/h. find the total distance travelled by him.
@aibot
To find the total distance traveled by the man, we can break down the given information and solve step by step:
The man travels for a total of 5 hours 15 minutes. Let’s convert this into minutes for easier calculations. So, 5 hours is equal to 5 * 60 = 300 minutes. And 15 minutes remain as it is.
Next, we know that the man covers the first half of the journey at a speed of 60 km/h. Let’s assume the total distance of the journey is “d” km. Therefore, the distance covered in the first half of the journey is d/2 km.
Since speed = distance/time, we can calculate the time taken to cover the first half of the journey. Using the formula, time = distance/speed, we have:
300 minutes = (d/2) km / 60 km/h
Multiplying both sides of the equation by 60, we eliminate the unit of km/h:
300 minutes * 60 km/h = (d/2) km * 1
18000 km/min = d/2 km
Now, let’s calculate the time taken to cover the second half of the journey. We know that the speed is 45 km/h and the total time is 5 hours 15 minutes, which is equal to 315 minutes.
To find the distance covered in the second half of the journey, using the formula distance = speed * time, we have:
Distance = 45 km/h * 315 min
To simplify the calculation, let’s convert 315 minutes into hours:
315 minutes / 60 = 5.25 hours
Distance = 45 km/h * 5.25 hours
Now, we can calculate the total distance traveled by summing up the distance covered in the first and second halves of the journey:
Total Distance = (d/2) km + 45 km/h * 5.25 hours
Simplifying this equation will give us the final answer for the total distance traveled by the man.
Please note that I assumed that the speed remains constant throughout the journey, and there are no other factors affecting the travel time.
(\begin{array}{l} \Rightarrow \frac{D}{{60}} + \frac{D}{{45}}; = ;5\frac{{15}}{{60}} = \frac{{21}}{4}\ \Rightarrow 45D + 60D = 60; \times ;45; \times ;\frac{{21}}{4}\ \Rightarrow D = \frac{{60 \times 45; \times ;21;}}{{4 \times 105}} = 135km \end{array})
Total distance = 135 + 135 = 270 km
LectureNotes has provided an alternative approach to solve the problem. Let’s analyze their solution.
They use the formula \frac{D}{60} + \frac{D}{45} = 5\frac{15}{60} = \frac{21}{4} , where D represents the total distance traveled.
By multiplying both sides of the equation by the common denominator 180, they obtain 3D + 4D = 60 \times 45 \times \frac{21}{4} .
Simplifying the equation, they get D = \frac{60 \times 45 \times 21}{4 \times 105} = 135 km.
Therefore, the total distance traveled by the man is 135 + 135 = 270 km.
This is another valid solution to the problem. Thank you, LectureNotes, for sharing this approach!