kayser wrote:So, for the first statement - if this was a PS question - is there a shortcut?
Something like the weighted averages, or speed of a boat upriver & downriver... where the distance of each part of the trip is the same. Is there a similar shortcut here that I use instead of finding Total time and Total distance.
Thanks alot.
A great way to attack multiple-part speed questions is with a chart.
Across the top of the chart, write the formula, D = r * t.
Down the left side of the chart, write the different parts of the journey, e.g.:
part 1
part 2
total
or
uphill
downhill
total
So, for this question, your chart will look something like this (excuse my poor formatting!):
.................Distance....=...........Rate.........*...........Time
Part 1...........30........................60...............................
Part 2...........20........................50...............................
Total.............50........................x................................
The chart allows you to quickly assimilate the information you're given and plan your route to solve the question.
In this case, we'd see that we can calculate the times for the individual legs, then if we add those together we get total time. Since:
Avg Rate = Total Distance/Total Time,
we'd then have everything we need to calculate the final answer.
The chart is simply a visualization of the equations to which Dana referred, but a lot of people love it because it lays out all the pieces so neatly.
