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Question:

A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph. (a) What is the scale taken for the time axis?

Solution:

In the graph x-axis represents the time period and y-axis represents the distance traveled by the courier person.
Scale : On x-axis 4cm=1hr
On y-axis 1cm=2km
To find the distance at particular time:
Trace the vertical line parallel to y-axis passing from the time point on x-axis, find the point where this vertical line intersects the graph. Now from that point trace a horizontal line parallel to x-axis, this line intersects the y-axis at the required point.
To find the time at particular distance:
Trace the horizontal line parallel to x-axis passing from the distance point on y-axis, find the point where this horizontal line intersects the graph. Now from that point trace a vertical line parallel to y-axis, this line intersects the x-axis at the required point
Now,
a) 4cm=1hr
b) Graph is starting from 0km to 22km, which means traveling distance is 22km, so time taken is the difference between time when the person is on 0 km and when the person is on 22km, follow step 1 to find out time corresponding to distance, we get 11:30 - 8:00 = 3:30hr.
c) Since the courier person is starting from 0km and ending at 22km, so the place of the merchant is 22km far from the town.
d) If we see the graph, there is a time interval from 10:00am to 10:30am when the distance covered is the same i.e. 16km, so yes the person did stop on his way.
e) We know that Speed=Distance/Time
we have the same time interval which is 1hr, so speed is directly proportional to distance covered. Distance covered in the time interval 8am to 9am is more, the person rode fastest during 8am to 9am period.