Here is a speed-time graph for a train - Edexcel - GCSE Maths - Question 18 - 2017 - Paper 3

To estimate the distance travelled by the train, we will use 4 strips of equal width on the speed-time graph.

1. Determine the width of each strip: The time interval is from 0 to 20 seconds. Given that we are to use 4 strips, each strip will have a width of:

   $ext{Width} = \frac{20 \text{ seconds}}{4} = 5 \text{ seconds}$

2. Estimate the heights (speeds) for each strip:

   • For the first strip (0s to 5s): Read the graph at 5 seconds, where speed is approximately 10 m/s.
   • For the second strip (5s to 10s): Read the graph at 10 seconds, where speed is approximately 15 m/s.
   • For the third strip (10s to 15s): Read the graph at 15 seconds, where speed is approximately 20 m/s.
   • For the fourth strip (15s to 20s): Read the graph at 20 seconds, where speed is approximately 25 m/s.

3. Calculate the area for each strip:

   • Area of strip 1 = Base × Height = 5s × 10m/s = 50 m
   • Area of strip 2 = 5s × 15m/s = 75 m
   • Area of strip 3 = 5s × 20m/s = 100 m
   • Area of strip 4 = 5s × 25m/s = 125 m

4. Sum the areas of the strips to find the total distance travelled:

   $ext{Total Distance} = 50 + 75 + 100 + 125 = 350 \text{ m}$

Thus, the estimated distance the train travelled in the first 20 seconds is 350 m.