Question

Ajit rides a scooter constantly at a speed of 30 Kms/hour. Draw a Time-distance graph for this situation. Use it to find
(a) the time taken by Ajit to ride 75 Km
(b) the distance covered by Ajit in \[3\dfrac{1}{2}\]hours.

Answer 1

Hint: This type of problem can be solved using graphs. To draw the graph we need different values of distance at different values of time. We can find this by using the given data and distance formula. By the obtained data we can plot a time versus distance graph. (\[3\dfrac{1}{2}\]We need to convert this into improper fraction, we get 3.5)

Complete step-by-step answer:
Given,
Speed of scooter=30 Kms/hour
We know the formula for distance is \[ \Rightarrow {\text{Distance = speed}} \times {\text{time}}\]
To make a distance time graph we need different values of distance at different values of times.

Time	\[{\text{Distance = speed}} \times {\text{time}}\]
1 hour	\[{\text{30}} \times {\text{1 = 30km}}\]
2 hours	\[{\text{30}} \times 2{\text{ = 60km}}\]
3 hours	\[{\text{30}} \times 3{\text{ = 90km}}\]
4 hours	\[{\text{30}} \times {\text{1 = 1200km}}\]

(We needed the time up to 3.5 hours so we stopped at 4 hours)
Now using this data we can plot a graph:

Time (in hour)	1	2	3	4
Distance (in Km	30	60	90	120

We set a scale:
X-axis=1 unit= 0.5 unit
Y-axis=1 unit=5 unit

Now,
(a) The time taken by Ajit to ride 75 Km.
See the graph below, we marked the Y-axis at 75 and drew a straight line until it cut the line that we obtained from given data. Corresponding X-axis values will be your required time in an hour. That is 2.5 hours.
Hence, the time taken by Ajit to ride 75 Km is 2.5 hours.

b) The distance covered by Ajit in \[3\dfrac{1}{2}\]hours.
That is the distance cover in 3.5 hours. We mark the X-axis at 75 and draw a straight line until it cuts the line that we obtained from given data. Corresponding Y-axis value will be your required distance covered in 3.5 hours. That is 105 km.
The distance covered by Ajit in \[3\dfrac{1}{2}\]hours is 105 km.

Note: We took a scale on Y-axis=1 unit=5 units so that we can get the exact values. We can also take to 10 units which will be easy to draw, but while finding distance using graphs it will seem quite difficult. While solving this kind of problem in graphs there will be no calculation part. Careful while assigning the points in a graph.