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Train A travels 120 km at a constant speed of 80 km/h - OCR - GCSE Maths - Question 8 - 2021 - Paper 1
Question 8
Train A travels 120 km at a constant speed of 80 km/h. Train B travels 120 km at a constant speed of 50 km/h. How many more minutes does train B take to travel 120 ... show full transcript
Worked Solution & Example Answer:Train A travels 120 km at a constant speed of 80 km/h - OCR - GCSE Maths - Question 8 - 2021 - Paper 1
Step 1
How many more minutes does train B take to travel 120 km than train A?
Answer
To determine the time taken by each train, we can use the formula for time:
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Calculate the time for Train A:
- Distance = 120 km
- Speed = 80 km/h
- Time for Train A = ( \frac{120}{80} = 1.5 ) hours
- To convert hours into minutes, multiply by 60:
- Time for Train A in minutes = ( 1.5 \times 60 = 90 ) minutes
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Calculate the time for Train B:
- Distance = 120 km
- Speed = 50 km/h
- Time for Train B = ( \frac{120}{50} = 2.4 ) hours
- To convert hours into minutes, multiply by 60:
- Time for Train B in minutes = ( 2.4 \times 60 = 144 ) minutes
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Calculate the difference in time:
- Difference = Time for Train B - Time for Train A
- Difference = 144 minutes - 90 minutes = 54 minutes
Thus, Train B takes 54 minutes longer than Train A.
Step 2
Write an algebraic expression for train C's speed in metres per second.
Answer
To convert the speed from kilometers per hour (km/h) to metres per second (m/s), we can use the conversion factor:
1 km/h = ( \frac{1000}{3600} ) m/s = ( \frac{1}{3.6} ) m/s
Therefore, for Train C which has a speed of x km/h:
- Speed in m/s = ( x \times \frac{1}{3.6} ) = ( \frac{x}{3.6} ) m/s
So, an appropriate algebraic expression for Train C's speed in metres per second is ( \frac{x}{3.6} ).