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# Calculating and estimating pace

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The y axis represents the distance traveled in kilometers and the horizontal axis is the time it took in hours.

a. Calculate the walking pace of A in relation to that of B

(my apologies if it's against the rules to publish a post twice ;c maybe someone who can help me sees it now)

May 17, 2020

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Speed= distance travelled / time taken.

Since A and B have both travelled 8km (vertical axis) in 8 hours (horizontal axis) there average speed over the 8 hours is identical.

However

Since at any given moment in time, velocity = distance/ time where the unit of time is approaching zero.

This means that velocity at any given point is given by the GRADIENT of the tangent to the curve at that point.

Your B curve is linear so the gradient is always the same. Velocity=speed= 8/8 = 1km/hour

The A pace changes.

Perhaps you can tell me what is happening. When is the gradient of the A curve equal, less, or greater  than that of the B curve ?

May 17, 2020
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In the first four hours A moves at a slower pace and then he speeds up? I'm not quite sure how to convert this into an 1 km/h format though

Guest May 17, 2020
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Yes that is right. Initially the gradient of A is less than B, and then about half way along it gets stepper which means it is going faster.

So they have about the same pace at 2.5 hours then again when?

So from 0 to 2.5 hours A is walking more slowly than B,     then from 2.5 to how many hours is A walking faster than B?

Part a is only asking for a comparison. It is asking which one is faster or slower and when that is happening.

Melody  May 17, 2020
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Oh I see, I thought they asked for an actual calculation. The pace is the same at 5.5 hours! Thank you for the help Melody!

Guest May 17, 2020
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Yes, although I would go for 5:45 (I mean 45 minutes) myself

You are very welcome.

I come here to help people learn and I think I have done that here so I am happy.

Melody  May 17, 2020
edited by Melody  May 17, 2020