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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?
(b) How much time did the person take for the travel?
(c) How far is the place of the merchant from the town?
(d) Did the person stop on his way? Explain.
(e) During which period did he ride fastest?
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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 $$4$$ cm $$= 1$$ hr
On $$y-$$axis $$1$$ cm $$= 2$$ km

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 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 required point

Now,
a) $$4$$ cm $$= 1$$ hr

b) Graph is starting from $$0$$ km to $$22$$ km, which means travelling distance is $$22$$ km, so time taken is difference between time when person is on 0 km and when person is on $$22$$ km, follow step 1 to find out time corresponding to distance, we get $$11:30 - 8= 3:30$$ hr.

c) Since courier person is starting from $$0$$ km and ending at $$22$$ km, so the place of merchant is $$22$$ km far from the town.

d) If we see the graph, there is a time interval from $$10:00$$ am to $$10:30$$ am when the distance covered is same i.e. $$16$$ km, so yes the person did stop on his way.

e) We know that Speed $$=\dfrac{\text{Distance}}{\text{Time}}$$    

we have same time interval which is $$1$$ hr, so speed is directly proportional to distance covered. 
Distance covered in time interval $$8$$ am to $$9$$ am is more person ride fastest during $$8$$ am to $$9$$ am period.

Mathematics
NCERT
Standard VIII

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