Video: Pack 1 • Paper 3 • Question 5

Pack 1 • Paper 3 • Question 5

06:18

Video Transcript

At seven am, a rain storm began. From seven am to 7:48 am, the amount of rain that fell was 12 millimeters. From 7:48 am to 8:18 am, rain fell at an average of 38 millimeters per hour. Part a) draw a graph to show the rainfall during the storm.

And in questions like this in the absence of other information, we need to assume that we got a constant rate of rainfall. And that means that the graph will consist of straight line segments between the key points. Now, the first thing we’re gonna do is create a little table.

You notice that the 𝑥-axis on the graph is time and the 𝑦-axis is the amount of rain in millimeters. The question says that the rain storm began at seven am. So at that point, no rain had fallen. So the total amount of rain was zero millimeters. And between seven and 7: 48 am, 12 millimeters of rain fell. So by 7:48 am, there was 12 millimeters. Then, between 7:48 and 8:18, rain fell at an average of 38 millimeters per hour.

Well, we need to ask ourselves, “How many hours are there between 7:48 and 8:18?” Well, between 7:48 and 7:50, there are two minutes and between 7:50 and eight, there are 10 minutes. So in total, between 7:48 and eight am, there are 12 minutes. And between eight am and 8:18 am. there are 18 minutes. That means in total between 7:48 and 8:18, there are 12 plus 18. That’s 30 minutes, which is 0.5 or half an hour.

Now, rain was falling at a rate of 38 millimeters per hour. That means in one hour, we’d have got 38 millimeters of rain. So in half an hour, we’d have got half that amount. And half of 38 is 19. So in that time, 19 millimeters of rain fell. But we got to remember 12 millimeters had already fallen. So by 8:18, a total of 12 plus 19 that’s 31 millimeters of rain had fallen.

Now, rather than drawing the graph like this, let’s zoom in so we can get a more accurate picture. But before we can go much further with this, we need to look very carefully at the scales on the axes. On the 𝑥-axis between seven am and 7:30 am, there are one, two, three, four, five, six, seven, eight, nine, 10 ticks. And those 10 ticks represent 30 minutes. So each individual tick represents 30 divided by 10 that’s three minutes. Then, on the vertical scale, between zero and five, we’ve got one, two, three, four, five, six, seven, eight, nine, 10 ticks again. So each tick represents five divided by 10 that’s 0.5 millimeters. In other words, two ticks vertically represent one millimeter of rain.

Okay, now, we’re ready to mark on the points. So at seven am, there was zero millimeters of rain. So that’s this point here. And at 7:48 am, there was 12 millimeters of rain. So we need to find 7:48. Well, 7:30 is here. So we can count up in threes: 33, 36, 39, 42, 45, 48. So the 𝑥-coordinate is 7:48 and the point is gonna be somewhere on that line. And 10 millimeters is here. So 11 millimeters is here two ticks later. And 12 milliliters is here two ticks after that. So our point is gonna be on the intersection of those two lines — that’s here.

So we’ve done this point and this point. We’ve just got the last point left to go — 8:18. Well, eight o’clock is here. Then, we can count up in threes: three, six, nine, 12, 15, 18. And our next point is gonna be somewhere on that line. And the 𝑦-coordinate is 31. So there’s 30, two ticks later is 31. So our next point is gonna be on the intersection of those two lines. Now remember we were assuming a constant rate of rainfall. So we can join all these points with a straight line and likewise between 7:48 and 8:18 am.

And now for part b, from 8:18 am to 9:33 am, a further 22.5 millimeters of rain fell. Work out the average rate of rainfall in millimeters per hour from 8:18 to 9:33 am.

Well, first let’s clear a little bit of space for the answer to this one. Like before, we got to work out how much time there is between 8:18 and 9:33. Now between 8:18 and 8:20, there is 22 minutes and between 8:20 and nine am, there are 40 minutes. So in total, between 8:18 and nine am, there are 42 minutes and between nine am and 9:33 am, there are 33 minutes. That means in total between 8:18 am and 9:33 am, there are 42 plus 33 minutes which is 75 minutes.

But the question asked for the rate of rainfall in millimeters per hour. So we’ve got to convert our minutes into hours. And since there are 60 minutes in an hour, we got to do 75 divided by 60 to work out the number of hours: 75 divided by 60 is 1.25. So there are 1.25 hours in that time interval and 22.5 millimeters of rainfall in that time. So 22.5 millimeters fall in 1.25 hours.

We want to know how much rain falls in one hour. Well, we convert 1.25 hours into one hour by dividing by 1.25. So if we divide the amount of time by 1.25, the amount of rain that falls also needs to be divided by 1.25. And 22.5 divided by 1.25 is 18 millimeters. So 18 millimeters fall in one hour. So the answer to part b is that the rate of rainfall is 18 millimeters per hour.