Two bus routes run past a transport hub near a corner shop. Route X departs every \(2^1\) minutes, while Route Y departs every \(2^{-1}\) hours. The hub man...
Question 1 Report
Two bus routes run past a transport hub near a corner shop. Route X departs every \(2^1\) minutes, while Route Y departs every \(2^{-1}\) hours. The hub manager compares both intervals before adjusting the printed timetable.
- Work out the interval for Route X in minutes. (1)
- Work out the interval for Route Y in minutes. (2)
- Find how many Route X buses depart in the time between two consecutive Route Y buses. (2)
Answer Details
This question compares two bus intervals given in different units, so a unit conversion is needed before the intervals can be compared directly.
(a) Route X's interval is \(2^1\) minutes: \[ 2^1 = 2 \text{ minutes} \] [1 mark]
(b) Route Y's interval is \(2^{-1}\) hours; evaluate the power first, then convert to minutes: \[ 2^{-1} \text{ hours} = \frac{1}{2} \text{ hour} = 0.5 \times 60 = 30 \text{ minutes} \] [2 marks]
(c) With both intervals in the same unit, divide the longer interval by the shorter one to count how many Route X buses fit between two Route Y buses: \[ 30 \div 2 = 15 \text{ buses} \] [2 marks]
The question is a reminder that index laws only combine values with a common base and common units; converting hours to minutes first is essential before any comparison or division makes sense.
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