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7. Helen cycles for 20 minutes at 5m/s and then for a further 10 minutes at 4m/s (a) How far does she cycle altogether? (b) Draw a distance-time graph for her ride

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7. Helen cycles for 20 minutes at 5m/s and then for a further 10 minutes at
4m/s
(a) How far does she cycle altogether?
(b) Draw a distance-time graph for her ride

7. Helen cycles for 20 minutes at 5m/s and then for a further 10 minutes at 4m/s (a) How far does she cycle altogether? (b) Draw a distance-time graph for her ride

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MeganElite · Tutor for 8 years

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(a) Helen cycles a total of 8400 meters. <br />(b) The distance-time graph would be a piecewise linear graph with two segments. The first segment is a line from (0,0) to (20,6000), and the second segment is a line from (20,6000) to (30,8400).

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## Step 1: Calculate the distance Helen cycles at 5 m/s<br />The distance Helen cycles at 5 m/s can be calculated using the formula for distance, which is speed multiplied by time. Given that Helen cycles at 5 m/s for 20 minutes, we first need to convert the time from minutes to seconds (since the speed is given in m/s). There are 60 seconds in a minute, so 20 minutes is 1200 seconds.<br /><br />### \(Distance = Speed \times Time = 5 m/s \times 1200 s = 6000 m\)<br /><br />## Step 2: Calculate the distance Helen cycles at 4 m/s<br />Similarly, the distance Helen cycles at 4 m/s can be calculated using the same formula. Given that Helen cycles at 4 m/s for 10 minutes, we first need to convert the time from minutes to seconds. 10 minutes is 600 seconds.<br /><br />### \(Distance = Speed \times Time = 4 m/s \times 600 s = 2400 m\)<br /><br />## Step 3: Calculate the total distance Helen cycles<br />The total distance Helen cycles is the sum of the distances she cycles at 5 m/s and 4 m/s.<br /><br />### \(Total Distance = Distance_{5m/s} + Distance_{4m/s} = 6000 m + 2400 m = 8400 m\)<br /><br />## Step 4: Draw a distance-time graph for her ride<br />The distance-time graph for Helen's ride would be a piecewise linear graph with two segments. The first segment would be a line from (0,0) to (20,6000), representing the first 20 minutes of her ride at 5 m/s. The second segment would be a line from (20,6000) to (30,8400), representing the next 10 minutes of her ride at 4 m/s.
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