A delivery van's odometer shows that a journey covers \(186\) km, correct to the nearest km. The journey took \(3.4\) hours, correct to 1 decimal place. Wri...
Question 1 Report
A delivery van's odometer shows that a journey covers \(186\) km, correct to the nearest km. The journey took \(3.4\) hours, correct to 1 decimal place.
- Write down the upper bound for the distance travelled. (1)
- Write down the lower bound for the time taken. (1)
- Work out the upper bound for the average speed of the van, giving your answer correct to 3 significant figures. (2)
Answer Details
The upper bound of a compound quantity like speed, formed by dividing distance by time, comes from dividing the largest possible distance by the smallest possible time, since making the numerator bigger and the denominator smaller both push the result upward.
(a) Rounded to the nearest km, half of 1 km is 0.5 km, so the upper bound of the distance is
\[186+0.5=186.5 \text{ km}\] [1 mark](b) Rounded to 1 decimal place, half of 0.1 hours is 0.05 hours, so the lower bound of the time is
\[3.4-0.05=3.35 \text{ hours}\] [1 mark](c) The upper bound of average speed uses the upper bound of distance divided by the lower bound of time:
\[186.5 \div 3.35 = 55.6716\ldots\]Rounded to 3 significant figures, this is \(55.7\) km/h. [2 marks]
Speed is distance divided by time, so its bounds behave oppositely for numerator and denominator: to maximise the result, the distance must be pushed to its upper bound while the time is pushed to its lower bound, and mixing this up is the most common error in bounds questions involving division.
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