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
b. Give an estimate of the time stamps on which A and B had the same pace. Please explain your answer.
(my apologies if it's against the rules to publish a post twice ;c maybe someone who can help me sees it now)
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.
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 ?
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
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.
About 2 and half hours from the start the gradient is about equal (parallel)
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.
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!