Increasing speed and decreasing time

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Quandaries & Queries

Question from Nigel, a student:

I am completely lost...can you help with this:

The time, t, to travel a distance, d, at a constant speed, v, can be obtained
from the formula: d = vt. If the speed is increased by x, find an expres-
sion to represent the decrease in time to travel the same distance.

Help!!

Hi Nigel.

Let's think of the two different situations: travelling slow and travelling fast:

d = vt t = d/v, so

t_s = d/v_s and t_f = d/v_f

since d is the same distance in both cases. What you are asked for is the decrease in time. That's the difference t_s - t_f:

t_s - t_f = d/v_s - d/v_f

Now, you also know that the increase in speed (v_f - v_s) is x, so can you finish the solution by substituting v for v_s and v + x for v_f and then simplifying?

Hope this helps,
Stephen La Rocque.

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