A train travels 165 km in 95 minutes and remaining 73 km in 1500 seconds. What is the average speed of the train?
119 km/hour
Understanding Average Speed
The question asks us to find the average speed of a train. Average speed is calculated by dividing the total distance traveled by the total time taken.
The formula for average speed is:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
Calculating Total Distance
The train travels in two parts:
- First part: 165 km
- Second part: 73 km
The total distance is the sum of these two distances.
\(\text{Total Distance} = 165 \text{ km} + 73 \text{ km}\)
\(\text{Total Distance} = 238 \text{ km}\)
Calculating Total Time
The time taken is given in two different units:
- First part: 95 minutes
- Second part: 1500 seconds
To find the total time, we need to convert both time durations into the same unit. Since the options for average speed are in km/hour, it is best to convert the time into hours.
Converting Time 1 (95 minutes) to Hours
There are 60 minutes in 1 hour. To convert minutes to hours, we divide by 60.
\(\text{Time}_1 = 95 \text{ minutes} = \frac{95}{60} \text{ hours}\)
\(\text{Time}_1 = \frac{19}{12} \text{ hours}\)
Converting Time 2 (1500 seconds) to Hours
There are 60 seconds in 1 minute and 60 minutes in 1 hour. So, there are \(60 \times 60 = 3600\) seconds in 1 hour. To convert seconds to hours, we divide by 3600.
\(\text{Time}_2 = 1500 \text{ seconds} = \frac{1500}{3600} \text{ hours}\)
\(\text{Time}_2 = \frac{15}{36} \text{ hours}\)
We can simplify the fraction \(\frac{15}{36}\) by dividing both numerator and denominator by their greatest common divisor, which is 3.
\(\text{Time}_2 = \frac{15 \div 3}{36 \div 3} \text{ hours} = \frac{5}{12} \text{ hours}\)
Calculating Total Time in Hours
Total time is the sum of Time 1 and Time 2.
\(\text{Total Time} = \text{Time}_1 + \text{Time}_2\)
\(\text{Total Time} = \frac{19}{12} \text{ hours} + \frac{5}{12} \text{ hours}\)
\(\text{Total Time} = \frac{19 + 5}{12} \text{ hours}\)
\(\text{Total Time} = \frac{24}{12} \text{ hours}\)
\(\text{Total Time} = 2 \text{ hours}\)
Calculating Average Speed
Now we have the total distance and the total time in the required units (km and hours).
- Total Distance = 238 km
- Total Time = 2 hours
Using the average speed formula:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{238 \text{ km}}{2 \text{ hours}}\)
\(\text{Average Speed} = 119 \text{ km/hour}\)
The average speed of the train is 119 km/hour.
Important Questions from Motion in a Straight Line
- Which of the following examples represents motion along a straight line?
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