Thread: Upper and Lower Bounds help

I don't understand the steps needed to complete the following question. A brief explanation will be appreciated!


1) A boy runs 50 metres at a speed of 5 m/s. Both values are measured to an accuracy of one sig. figure. What is the least possible time taken?


2) A crane has a cable with a breaking strain of 5300kg measured to 2 sig. figures. It is used to lift crates which weigh 10kg measured to the nearest 10kg.

What is the greatest number of crates than can be lifted at one time so that the cable does not break?


3) A coffee machine dispenses 130 millilitres of black coffee into cups with a capacity of 175 millilitres. These values are accurate to 3 sig. figures.

Milk is supplied in small cartons which contain 21 millilitres, accurate to the nearest millilitre.

Beryl likes milky coffeee and always puts 2 cartons of milk in her coffee.

will her cup ever overflow?

1) Since they are to an accuracy of 1 significant figures, it means that the distance could be 45 m or 54 m but it will be expressed as 50 m. In the same way, 5m/s could actually be 4.5 m/s or 5.4 m/s.

Time taken is given by Distance/Speed.

Which pair of information would give the lowest time?

2) Same thing for this one. The upper and lower bounds for the crane are 5250 kg and 5340 kg and that for the crates are 5 kg and 14 kg.

From this, the number of crates that can be raised by the crane is given by (Breaking strain)/(Weight of crate)

When is this the largest?

3) Care to try out this one?